Sesión 08

Experimentos repetidos en el tiempo

y en el espacio


Christian Vásquez-Velasco, Bach., M.Sc.(c)

InkaStats Academy

2023

Instalar paquetes necesarios


# install.packages("devtools")
# devtools::install_github("emitanaka/edibble", force = T)
# devtools::install_github("emitanaka/deggust", force = T)

if (!require("pacman")) install.packages("pacman")
pacman::p_load(readxl, agricolae, agricolaeplotr, car, tidyverse,
               PMCMRplus, 
               outliers, nortest, mvtnorm, lmtest, ExpDes,
               edibble, gt,
               gtsummary, devtools, deggust, xlsx, desplot,
               ggResidpanel, fastGraph, gvlma, multcomp,
               phia, dvmisc, GAD, emmeans)
package 'xlsx' successfully unpacked and MD5 sums checked

The downloaded binary packages are in
    C:\Users\cvasquezv\AppData\Local\Temp\Rtmpm493xe\downloaded_packages

Experimentos repetidos en el espacio


Análisis de DCA de dos vías repetido en el espacio


Importación de datos


archivos <- list.files(pattern = "datos exp. repetidos.xlsx", 
                       full.names = TRUE,
                       recursive = TRUE)

# Importación
data <- readxl::read_xlsx(archivos,
                           sheet = "espacio")

# Preprocesamiento

data <- data %>%
  mutate_if(is.character, factor) %>%
  mutate(Zona = GAD::as.fixed(factor(Zona)),
         DOSIS = GAD::as.fixed(factor(DOSIS)),
         VARIEDAD = GAD::as.fixed(factor(VARIEDAD)),
         BLOQUE = GAD::as.random(BLOQUE))

data_D <- data %>%
  dplyr::filter(DOSIS %in% 0)

Definición del modelo


modelo.dca1 <- lm(Diametro_tallo_90dds ~ Zona + BLOQUE %in% Zona +
                    VARIEDAD + VARIEDAD/Zona, data = data_D)
modelo.dca2 <- lm(Diametro_tallo_90dds ~ Zona + BLOQUE %in% Zona +
                    VARIEDAD, data = data_D)

Nota

  • La expresión “BLOQUE/ZONA” es para considerar la interacción como efecto fijo.
  • La expresión “BLOQUE:ZONA” es para considerar la interacción como efecto aleatorio.
  • La expresión “BLOQUE %in% ZONA” permite que se genere una estructura del análisis de varianza donde se anide el efecto de la variedad dentro de cada bloque
broom::glance(modelo.dca1) %>%
  bind_rows(broom::glance(modelo.dca2)) %>%
  dplyr::mutate(Modelo = c("Zona * Variedad + Bloque/Zona",
                           "Zona + Variedad + Bloque/Zona")) %>%
  dplyr::select(Modelo, AIC, BIC) %>%
  dplyr::arrange(BIC) %>%
  dplyr::mutate(Mérito = 1:n()) %>%
  dplyr::relocate(Mérito, Modelo) %>%
  gt()
Mérito Modelo AIC BIC
1 Zona + Variedad + Bloque/Zona -36.91794 -33.03869
2 Zona * Variedad + Bloque/Zona -35.21426 -30.85010
modelo.dca <- modelo.dca2
summary(modelo.dca)

Call:
lm(formula = Diametro_tallo_90dds ~ Zona + BLOQUE %in% Zona + 
    VARIEDAD, data = data_D)

Residuals:
        1         2         3         4         5         6         7         8 
 0.029167  0.029167 -0.045833 -0.029167 -0.029167  0.045833  0.004167 -0.020833 
        9        10        11        12 
 0.004167 -0.004167  0.020833 -0.004167 

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)             0.72083    0.03157  22.834    3e-06 ***
ZonaCastilla           -0.07500    0.04133  -1.815  0.12931    
VARIEDAD2              -0.04167    0.02386  -1.746  0.14123    
ZonaCamana:BLOQUEII     0.05000    0.04133   1.210  0.28046    
ZonaCastilla:BLOQUEII   0.17500    0.04133   4.234  0.00822 ** 
ZonaCamana:BLOQUEIII    0.07500    0.04133   1.815  0.12931    
ZonaCastilla:BLOQUEIII  0.05000    0.04133   1.210  0.28046    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.04133 on 5 degrees of freedom
Multiple R-squared:  0.8509,    Adjusted R-squared:  0.672 
F-statistic: 4.756 on 6 and 5 DF,  p-value: 0.05403

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dca)
ggResidpanel::resid_panel(modelo.dca)
influence.measures(modelo.dca)
Influence measures of
     lm(formula = Diametro_tallo_90dds ~ Zona + BLOQUE %in% Zona +      VARIEDAD, data = data_D) :

    dfb.1_  dfb.ZnCs dfb.VARI dfb.ZnCm.BLOQUEII dfb.ZnCs.BLOQUEII
1   1.3263 -8.68e-01  -0.5013         -8.68e-01          8.35e-17
2   0.1895 -7.42e-17  -0.5013          8.68e-01         -9.86e-17
3  -0.4057  7.98e-16   1.0735          5.36e-16          4.94e-17
4  -0.9473  8.68e-01  -0.5013          8.68e-01          9.15e-17
5   0.1895 -1.30e-16  -0.5013         -8.68e-01          7.69e-18
6  -0.4057  5.76e-16   1.0735          5.36e-16          1.47e-18
7   0.0237  1.08e-01  -0.0626         -1.91e-17         -1.08e-01
8  -0.1260  1.47e-16   0.3333          7.21e-17         -5.77e-01
9   0.0237 -7.72e-18  -0.0626         -2.54e-17          1.04e-17
10  0.0237 -1.08e-01  -0.0626         -1.02e-17          1.08e-01
11 -0.1260  8.62e-18   0.3333          9.99e-17          5.77e-01
12  0.0237 -2.27e-17  -0.0626         -3.91e-18         -1.04e-17
   dfb.ZnCm.BLOQUEIII dfb.ZnCs.BLOQUEIII  dffit   cov.r  cook.d   hat inf
1           -8.68e-01           0.00e+00  1.326  1.6911 0.23902 0.583   *
2           -1.45e-16           4.82e-17  1.326  1.6911 0.23902 0.583    
3           -1.86e+00           8.43e-17 -2.840  0.0222 0.59024 0.583   *
4            8.68e-01           2.33e-17 -1.326  1.6911 0.23902 0.583    
5           -1.69e-16           5.79e-17 -1.326  1.6911 0.23902 0.583    
6            1.86e+00           2.10e-17  2.840  0.0222 0.59024 0.583   *
7           -2.00e-17          -1.08e-01  0.166 11.0590 0.00488 0.583   *
8            1.44e-16          -2.05e-17 -0.882  4.6048 0.12195 0.583    
9           -2.21e-17           1.08e-01  0.166 11.0590 0.00488 0.583   *
10          -2.81e-17           1.08e-01 -0.166 11.0590 0.00488 0.583   *
11           1.44e-16           2.70e-17  0.882  4.6048 0.12195 0.583    
12          -2.61e-17          -1.08e-01 -0.166 11.0590 0.00488 0.583   *
influenceIndexPlot(modelo.dca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1      0.02235772     1.8536585  0.9140
   2     -0.35772358     2.4634146  0.1584
   3     -0.42073171     2.3414634  0.9168
   4      0.08943089     1.2195122  0.8212
   5      0.39227642     0.4634146  0.1348
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dca
DW = 1.8537, p-value = 0.9119
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.dca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dca)
W = 0.98058, p-value = 0.9859
ad.test(rstudent(modelo.dca))

    Anderson-Darling normality test

data:  rstudent(modelo.dca)
A = 0.19482, p-value = 0.861
lillie.test(rstudent(modelo.dca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dca)
D = 0.12277, p-value = 0.8862
ks.test(rstudent(modelo.dca), "pnorm",
        alternative = "two.sided")

    Exact one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dca)
D = 0.11883, p-value = 0.9881
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dca)
W = 0.029639, p-value = 0.8354
pearson.test(rstudent(modelo.dca))

    Pearson chi-square normality test

data:  rstudent(modelo.dca)
P = 2, p-value = 0.5724
sf.test(rstudent(modelo.dca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dca)
W = 0.97048, p-value = 0.8503

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 1.889962, Df = 1, p = 0.16921
bptest(modelo.dca)

    studentized Breusch-Pagan test

data:  modelo.dca
BP = 12, df = 6, p-value = 0.06197
bptest(modelo.dca, studentize = F)

    Breusch-Pagan test

data:  modelo.dca
BP = 5.9393, df = 6, p-value = 0.43
olsrr::ols_test_breusch_pagan(modelo.dca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

                      Data                       
 ------------------------------------------------
 Response : Diametro_tallo_90dds 
 Variables: fitted values of Diametro_tallo_90dds 

        Test Summary         
 ----------------------------
 DF            =    1 
 Chi2          =    1.889962 
 Prob > Chi2   =    0.1692062 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dca %>% gvlma()

Call:
lm(formula = Diametro_tallo_90dds ~ Zona + BLOQUE %in% Zona + 
    VARIEDAD, data = data_D)

Coefficients:
           (Intercept)            ZonaCastilla               VARIEDAD2  
               0.72083                -0.07500                -0.04167  
   ZonaCamana:BLOQUEII   ZonaCastilla:BLOQUEII    ZonaCamana:BLOQUEIII  
               0.05000                 0.17500                 0.07500  
ZonaCastilla:BLOQUEIII  
               0.05000  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                       Value p-value                Decision
Global Stat        5.213e+00  0.2661 Assumptions acceptable.
Skewness           1.568e-32  1.0000 Assumptions acceptable.
Kurtosis           5.102e-01  0.4751 Assumptions acceptable.
Link Function      2.589e+00  0.1076 Assumptions acceptable.
Heteroscedasticity 2.113e+00  0.1460 Assumptions acceptable.

Análisis de varianza

\[Y_{ijk} = \mu + \tau_{i} + \text{Error}(\tau\text{rep})_{i(k)} + \beta_{j} + \epsilon_{ijk}\]

\[\hat{Y}_{ijk} = \mu + \tau_{i} + \text{Error}(\tau\text{rep})_{i(k)} + \beta_{j}\]

Dónde:

\(Y_{ijk}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijk}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor Zona.

\(\text{Error}(\tau\text{rep})_{i(k)}\) = Efecto del i-ésimo nivel de Zona en el k-ésimo nivel de repetición.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor tratamiento (Variedad).

\(\epsilon_{ijk}\) = Residuo observado del modelo.

Pruebas de hipótesis

Para el factor A (Zona):

\(H_0: \tau_{A1} = \tau_{A2} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (Variedad):

\(H_0: \beta_{B1} = \beta_{B2} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dca, test = "F")
Analysis of Variance Table

Response: Diametro_tallo_90dds
            Df   Sum Sq   Mean Sq F value  Pr(>F)  
Zona         1 0.005208 0.0052083  3.0488 0.14123  
VARIEDAD     1 0.005208 0.0052083  3.0488 0.14123  
Zona:BLOQUE  4 0.038333 0.0095833  5.6098 0.04315 *
Residuals    5 0.008542 0.0017083                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
GAD::estimates(modelo.dca)
$tm
            Zona BLOQUE VARIEDAD        n
Zona           0      3        2 1.714286
VARIEDAD       2      3        0 1.714286
Zona:BLOQUE    1      1        2 1.714286
Res            1      1        1 1.000000

$mse
            Mean square estimates     
Zona        "Res + Zona:BLOQUE + Zona"
VARIEDAD    "Res + VARIEDAD"          
Zona:BLOQUE "Res + Zona:BLOQUE"       
Residual    "Res"                     

$f.versus
            F-ratio versus
Zona        "Zona:BLOQUE" 
VARIEDAD    "Residual"    
Zona:BLOQUE "Residual"    
GAD::gad(modelo.dca)
Analysis of Variance Table

Response: Diametro_tallo_90dds
            Df   Sum Sq   Mean Sq F value  Pr(>F)  
Zona         1 0.005208 0.0052083  0.5435 0.50190  
VARIEDAD     1 0.005208 0.0052083  3.0488 0.14123  
Zona:BLOQUE  4 0.038333 0.0095833  5.6098 0.04315 *
Residual     5 0.008542 0.0017083                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(Zona/rep)” en el caso de efectos aleatorios o “Error(Zona:rep)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos.

aov(Diametro_tallo_90dds ~ Zona + VARIEDAD + Error(BLOQUE %in% Zona), data = data_D) -> aov.dca
summary(aov.dca)

Error: BLOQUE:Zona
          Df  Sum Sq  Mean Sq F value Pr(>F)
Zona       1 0.00521 0.005208   0.543  0.502
Residuals  4 0.03833 0.009583               

Error: Within
          Df   Sum Sq  Mean Sq F value Pr(>F)
VARIEDAD   1 0.005208 0.005208   3.049  0.141
Residuals  5 0.008542 0.001708               
broom::tidy(aov.dca)
# A tibble: 4 × 7
  stratum     term         df   sumsq  meansq statistic p.value
  <chr>       <chr>     <dbl>   <dbl>   <dbl>     <dbl>   <dbl>
1 BLOQUE:Zona Zona          1 0.00521 0.00521     0.543   0.502
2 BLOQUE:Zona Residuals     4 0.0383  0.00958    NA      NA    
3 Within      VARIEDAD      1 0.00521 0.00521     3.05    0.141
4 Within      Residuals     5 0.00854 0.00171    NA      NA    
broom::tidy(gad(modelo.dca))
# A tibble: 4 × 6
  term           df   sumsq  meansq statistic p.value
  <chr>       <int>   <dbl>   <dbl>     <dbl>   <dbl>
1 Zona            1 0.00521 0.00521     0.543  0.502 
2 VARIEDAD        1 0.00521 0.00521     3.05   0.141 
3 Zona:BLOQUE     4 0.0383  0.00958     5.61   0.0432
4 Residual        5 0.00854 0.00171    NA     NA     

Valor de la tabla de F para el factor Zona con una significancia de 0.05.

qf(0.95, 1, 4)
[1] 7.708647

Valor de la tabla de F para el factor Variedad con una significancia de 0.05.

qf(0.95, 1, 5)
[1] 6.607891

Conclusión.

Con respecto al Factor Zona: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor Zona tienen un efecto sobre el diámetro de tallo estadísticamente similar a 0.

Con respecto al Factor Variedad: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor Variedad tienen un efecto sobre el diámetro de tallo estadísticamente similar a 0.

agricolae::cv.model(modelo.dca)
[1] 5.733918

Comparaciones de medias para los efectos principales del Factor Zona

get_df_ea <- function(object) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  df_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(":", stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(df)
  return(df_rep_A_residuals)
}
get_df_ea(aov.dca)
[1] 4
get_mse_ea <- function(object) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  meansq_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(":", stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(meansq)
  return(meansq_rep_A_residuals)
}
get_mse_ea(aov.dca)
[1] 0.009583333
data %>% with(LSD.test(
  Diametro_tallo_90dds, # Cambiar según nombre de variable respuesta
  Zona, # Cambiar según nombre de variable independiente
  DFerror = get_df_ea(aov.dca), 
  MSerror = get_mse_ea(aov.dca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: Diametro_tallo_90dds ~ Zona

LSD t Test for Diametro_tallo_90dds 

Mean Square Error:  0.009583333 

Zona,  means and individual ( 95 %) CI

         Diametro_tallo_90dds        std  r       LCL      UCL Min  Max
Camana              0.7270833 0.09205288 24 0.6716027 0.782564 0.5 0.90
Castilla            0.7395833 0.06753287 24 0.6841027 0.795064 0.6 0.85

Alpha: 0.05 ; DF Error: 4
Critical Value of t: 2.776445 

least Significant Difference: 0.07846153 

Treatments with the same letter are not significantly different.

         Diametro_tallo_90dds groups
Castilla            0.7395833      a
Camana              0.7270833      a

Comparaciones de medias para los efectos principales del Factor Variedad

data %>% with(LSD.test(
  Diametro_tallo_90dds, # Cambiar según nombre de variable respuesta
  VARIEDAD, # Cambiar según nombre de variable independiente
  DFerror = df.residual(modelo.dca), 
  MSerror = dvmisc::get_mse(modelo.dca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: Diametro_tallo_90dds ~ VARIEDAD

LSD t Test for Diametro_tallo_90dds 

Mean Square Error:  0.001708333 

VARIEDAD,  means and individual ( 95 %) CI

  Diametro_tallo_90dds        std  r       LCL      UCL Min  Max
1            0.7583333 0.07322786 24 0.7366457 0.780021 0.6 0.90
2            0.7083333 0.08030738 24 0.6866457 0.730021 0.5 0.85

Alpha: 0.05 ; DF Error: 5
Critical Value of t: 2.570582 

least Significant Difference: 0.03067094 

Treatments with the same letter are not significantly different.

  Diametro_tallo_90dds groups
1            0.7583333      a
2            0.7083333      b

Comparaciones de medias para las interacciones

Para los niveles del factor A dentro del nivel B1:

  • A1 vs A2:

\(H_0: \mu_{A1} - \mu_{A2} = 0\)

\(H_1: \mu_{A1} - \mu_{A2} \neq 0\)

Para los niveles del factor B dentro del nivel A1:

  • B1 vs B2:

\(H_0: \mu_{B1} - \mu_{B2} = 0\)

\(H_1: \mu_{B1} - \mu_{B2} \neq 0\)

NOTA: Repetir este proceso para cada nivel de A y cada nivel de B.

Análisis de varianza para interacción de dos factores con el paquete phia

Comparación de los niveles de B dentro de cada nivel de A

phia::testInteractions(modelo.dca,
                       fixed = "Zona",
                       across = "VARIEDAD",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
             Value Df Sum of Sq      F Pr(>F)
  Camana  0.041667  1 0.0052083 3.0488 0.1412
Castilla  0.041667  1 0.0052083 3.0488 0.1412
Residuals           5 0.0085417              

Comparación de los niveles de A dentro de cada nivel de B

phia::testInteractions(modelo.dca,
                       fixed = "VARIEDAD",
                       across = "Zona",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
             Value Df Sum of Sq      F Pr(>F)
1         0.041667  1 0.0052083 3.0488 0.1412
2         0.041667  1 0.0052083 3.0488 0.1412
Residuals           5 0.0085417              

Plot de interacciones

phia::interactionMeans(model = modelo.dca,
                       factors = c("Zona","VARIEDAD")) %>%
  plot()

Comparaciones de medias de los niveles de B dentro de cada nivel de A

filter_by_2factor_level <- function(data, factor_name1, factor_name2) {
  levels1 <- levels(data[[deparse(substitute(factor_name1))]])
  filters1 <- purrr::map(levels1, ~ filter(data, {{factor_name1}} == .x))
  names(filters1) <- levels1
  
  levels2 <- levels(data[[deparse(substitute(factor_name2))]])
  filters2 <- purrr::map(levels2, ~ filter(data, {{factor_name2}} == .x))
  names(filters2) <- levels2
  
  result <- list()
  result[[deparse(substitute(factor_name1))]] <- filters1
  result[[deparse(substitute(factor_name2))]] <- filters2
  return(result)
}
datos_filtrados <- filter_by_2factor_level(data = data,
                       factor_name1 = Zona,
                       factor_name2 =  VARIEDAD)
multcomp.test_2factors <- function(object, respuesta, factor_name1, factor_name2, test, aov){
  
  # Función auxiliar para aplicar la prueba de comparaciones múltiples a un data frame
  multcomp_df <- function(df, respuesta, factor_name, test, aov){
    if (test == "LSD") {
      comp <- LSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "HSD") {
      comp <- HSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "duncan") {
      comp <- duncan.test(df[[respuesta]],
                          df[[factor_name]],
                          DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                          group=TRUE,
                          main = NULL,
                          console=FALSE)[[6]]
    } else if (test == "SNK") {
      comp <- SNK.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[6]]
    } else {
      stop("Test no válido. Los tests disponibles son LSD, HSD, duncan, y SNK.")
    }
    
    return(comp %>%
             rename("y" = "df[[respuesta]]")
           )
  }
  
  # Aplicar la prueba de comparaciones múltiples a todos los data frames dentro de filters1
  comp_filters1 <- lapply(object[[1]], function(df){
    multcomp_df(df, respuesta, factor_name2, test, aov) %>%
      arrange(row.names(.)) %>%
      rownames_to_column(var = "x") %>%
      relocate(x)
  })
  
  # Aplicar la prueba de comparaciones múltiples a todos los data frames dentro de filters2
  comp_filters2 <- lapply(object[[2]], function(df){
    multcomp_df(df, respuesta, factor_name1, test, aov) %>%
      dplyr::arrange(row.names(.)) %>%
      rownames_to_column(var = "x") %>%
      relocate(x) %>%
      dplyr::mutate(groups = toupper(groups))
  })
  
  row.names(comp_filters1) <- NULL
  row.names(comp_filters2) <- NULL
  # Retornar una lista con las comparaciones múltiples para cada data frame
  result <- list()
  result[[as.name(substitute(factor_name1))]] <- comp_filters1
  result[[as.name(substitute(factor_name2))]] <- comp_filters2
  return(#list(#"Comparación de los niveles del factor B dentro de cada nivel del factor A",
         result#[[1]],
         # "Comparación de los niveles del factor A dentro de cada nivel del factor B",
         # result[[2]]
         # )
  )
}
multcomp.test_2factors(
  object = datos_filtrados,
  respuesta = "Diametro_tallo_90dds",
  factor_name1 = "Zona",
  factor_name2 = "VARIEDAD",
  test = "LSD",
  aov = modelo.dca) -> result.comp
result.comp
$Zona
$Zona$Camana
  x         y groups
1 1 0.7708333      a
2 2 0.6833333      b

$Zona$Castilla
  x         y groups
1 1 0.7458333      a
2 2 0.7333333      a


$VARIEDAD
$VARIEDAD$`1`
         x         y groups
1   Camana 0.7708333      A
2 Castilla 0.7458333      A

$VARIEDAD$`2`
         x         y groups
1   Camana 0.6833333      B
2 Castilla 0.7333333      A
# Convertir la lista a un data frame
df <- result.comp %>%
  reshape2::melt() %>% 
  ungroup() %>%
  dplyr::select(-variable) %>%
  relocate("Factor" = "L1",
           "Nivel" = "L2",
           x,
           "y" = "value",
           groups)
df
    Factor    Nivel        x         y groups
1     Zona   Camana        1 0.7708333      a
2     Zona   Camana        2 0.6833333      b
3     Zona Castilla        1 0.7458333      a
4     Zona Castilla        2 0.7333333      a
5 VARIEDAD        1   Camana 0.7708333      A
6 VARIEDAD        1 Castilla 0.7458333      A
7 VARIEDAD        2   Camana 0.6833333      B
8 VARIEDAD        2 Castilla 0.7333333      A
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # # Convertir level1 y level2 en nombres simbólicos
  # level1 <- as.name(level1)
  # level2 <- as.name(level2)
  # 
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1, level2)) %>%
    dplyr::mutate(groups = paste0(groups.y,groups.x)) %>%
    dplyr::select(!!level1,!!level2, y, groups) #%>%
    # rename(!!level1 := x,
    #        !!level2 := Nivel)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
df2 <- create_report(df = df,
               level1 = "Zona",
               level2 = "VARIEDAD") 
df2 %>% gt()
Zona VARIEDAD y groups
Camana 1 0.7708333 Aa
Camana 2 0.6833333 Bb
Castilla 1 0.7458333 Aa
Castilla 2 0.7333333 Aa
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1,level2)) %>%
    dplyr::mutate(y = paste0(round(y,2), " ", groups.y, groups.x)) %>%
    dplyr::select(!!level1,!!level2, y)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
df3 <- create_report(df = df,
               level1 = "Zona",
               level2 = "VARIEDAD") 
df3 %>% gt()
Zona VARIEDAD y
Camana 1 0.77 Aa
Camana 2 0.68 Bb
Castilla 1 0.75 Aa
Castilla 2 0.73 Aa
df3 %>% 
 pivot_wider(names_from = VARIEDAD,
             values_from = c(y), 
             names_glue = "{VARIEDAD}") %>%
  gt()
Zona 1 2
Camana 0.77 Aa 0.68 Bb
Castilla 0.75 Aa 0.73 Aa

Análisis de DBCA de dos vías repetido en el espacio


Definición del modelo


modelo.dbca1 <- lm(Diametro_tallo_90dds ~ BLOQUE + Zona + BLOQUE %in% Zona +
                    VARIEDAD + BLOQUE + VARIEDAD/Zona, data = data_D)
modelo.dbca2 <- lm(Diametro_tallo_90dds ~ Zona + BLOQUE %in% Zona +
                    VARIEDAD, data = data_D)

Nota

  • La expresión “BLOQUE/ZONA” es para considerar la interacción como efecto fijo.
  • La expresión “BLOQUE:ZONA” es para considerar la interacción como efecto aleatorio.
  • La expresión “BLOQUE %in% ZONA” permite que se genere una estructura del análisis de varianza donde se anide el efecto de la variedad dentro de cada bloque
broom::glance(modelo.dbca1) %>%
  bind_rows(broom::glance(modelo.dbca2)) %>%
  dplyr::mutate(Modelo = c("Zona * Variedad + Bloque/Zona",
                           "Zona + Variedad + Bloque/Zona")) %>%
  dplyr::select(Modelo, AIC, BIC) %>%
  dplyr::arrange(BIC) %>%
  dplyr::mutate(Mérito = 1:n()) %>%
  dplyr::relocate(Mérito, Modelo) %>%
  gt()
Mérito Modelo AIC BIC
1 Zona + Variedad + Bloque/Zona -36.91794 -33.03869
2 Zona * Variedad + Bloque/Zona -35.21426 -30.85010
modelo.dbca <- modelo.dbca2
summary(modelo.dbca)

Call:
lm(formula = Diametro_tallo_90dds ~ Zona + BLOQUE %in% Zona + 
    VARIEDAD, data = data_D)

Residuals:
        1         2         3         4         5         6         7         8 
 0.029167  0.029167 -0.045833 -0.029167 -0.029167  0.045833  0.004167 -0.020833 
        9        10        11        12 
 0.004167 -0.004167  0.020833 -0.004167 

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)             0.72083    0.03157  22.834    3e-06 ***
ZonaCastilla           -0.07500    0.04133  -1.815  0.12931    
VARIEDAD2              -0.04167    0.02386  -1.746  0.14123    
ZonaCamana:BLOQUEII     0.05000    0.04133   1.210  0.28046    
ZonaCastilla:BLOQUEII   0.17500    0.04133   4.234  0.00822 ** 
ZonaCamana:BLOQUEIII    0.07500    0.04133   1.815  0.12931    
ZonaCastilla:BLOQUEIII  0.05000    0.04133   1.210  0.28046    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.04133 on 5 degrees of freedom
Multiple R-squared:  0.8509,    Adjusted R-squared:  0.672 
F-statistic: 4.756 on 6 and 5 DF,  p-value: 0.05403

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dbca)
ggResidpanel::resid_panel(modelo.dbca)
influence.measures(modelo.dbca)
Influence measures of
     lm(formula = Diametro_tallo_90dds ~ Zona + BLOQUE %in% Zona +      VARIEDAD, data = data_D) :

    dfb.1_  dfb.ZnCs dfb.VARI dfb.ZnCm.BLOQUEII dfb.ZnCs.BLOQUEII
1   1.3263 -8.68e-01  -0.5013         -8.68e-01          8.35e-17
2   0.1895 -7.42e-17  -0.5013          8.68e-01         -9.86e-17
3  -0.4057  7.98e-16   1.0735          5.36e-16          4.94e-17
4  -0.9473  8.68e-01  -0.5013          8.68e-01          9.15e-17
5   0.1895 -1.30e-16  -0.5013         -8.68e-01          7.69e-18
6  -0.4057  5.76e-16   1.0735          5.36e-16          1.47e-18
7   0.0237  1.08e-01  -0.0626         -1.91e-17         -1.08e-01
8  -0.1260  1.47e-16   0.3333          7.21e-17         -5.77e-01
9   0.0237 -7.72e-18  -0.0626         -2.54e-17          1.04e-17
10  0.0237 -1.08e-01  -0.0626         -1.02e-17          1.08e-01
11 -0.1260  8.62e-18   0.3333          9.99e-17          5.77e-01
12  0.0237 -2.27e-17  -0.0626         -3.91e-18         -1.04e-17
   dfb.ZnCm.BLOQUEIII dfb.ZnCs.BLOQUEIII  dffit   cov.r  cook.d   hat inf
1           -8.68e-01           0.00e+00  1.326  1.6911 0.23902 0.583   *
2           -1.45e-16           4.82e-17  1.326  1.6911 0.23902 0.583    
3           -1.86e+00           8.43e-17 -2.840  0.0222 0.59024 0.583   *
4            8.68e-01           2.33e-17 -1.326  1.6911 0.23902 0.583    
5           -1.69e-16           5.79e-17 -1.326  1.6911 0.23902 0.583    
6            1.86e+00           2.10e-17  2.840  0.0222 0.59024 0.583   *
7           -2.00e-17          -1.08e-01  0.166 11.0590 0.00488 0.583   *
8            1.44e-16          -2.05e-17 -0.882  4.6048 0.12195 0.583    
9           -2.21e-17           1.08e-01  0.166 11.0590 0.00488 0.583   *
10          -2.81e-17           1.08e-01 -0.166 11.0590 0.00488 0.583   *
11           1.44e-16           2.70e-17  0.882  4.6048 0.12195 0.583    
12          -2.61e-17          -1.08e-01 -0.166 11.0590 0.00488 0.583   *
influenceIndexPlot(modelo.dbca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dbca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1      0.02235772     1.8536585  0.8804
   2     -0.35772358     2.4634146  0.1484
   3     -0.42073171     2.3414634  0.9448
   4      0.08943089     1.2195122  0.8196
   5      0.39227642     0.4634146  0.1224
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dbca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dbca
DW = 1.8537, p-value = 0.9119
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.dbca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dbca)
W = 0.98058, p-value = 0.9859
ad.test(rstudent(modelo.dbca))

    Anderson-Darling normality test

data:  rstudent(modelo.dbca)
A = 0.19482, p-value = 0.861
lillie.test(rstudent(modelo.dbca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dbca)
D = 0.12277, p-value = 0.8862
ks.test(rstudent(modelo.dbca), "pnorm",
        alternative = "two.sided")

    Exact one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dbca)
D = 0.11883, p-value = 0.9881
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dbca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dbca)
W = 0.029639, p-value = 0.8354
pearson.test(rstudent(modelo.dbca))

    Pearson chi-square normality test

data:  rstudent(modelo.dbca)
P = 2, p-value = 0.5724
sf.test(rstudent(modelo.dbca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dbca)
W = 0.97048, p-value = 0.8503

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dbca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 1.889962, Df = 1, p = 0.16921
bptest(modelo.dbca)

    studentized Breusch-Pagan test

data:  modelo.dbca
BP = 12, df = 6, p-value = 0.06197
bptest(modelo.dbca, studentize = F)

    Breusch-Pagan test

data:  modelo.dbca
BP = 5.9393, df = 6, p-value = 0.43
olsrr::ols_test_breusch_pagan(modelo.dbca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

                      Data                       
 ------------------------------------------------
 Response : Diametro_tallo_90dds 
 Variables: fitted values of Diametro_tallo_90dds 

        Test Summary         
 ----------------------------
 DF            =    1 
 Chi2          =    1.889962 
 Prob > Chi2   =    0.1692062 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dbca %>% gvlma()

Call:
lm(formula = Diametro_tallo_90dds ~ Zona + BLOQUE %in% Zona + 
    VARIEDAD, data = data_D)

Coefficients:
           (Intercept)            ZonaCastilla               VARIEDAD2  
               0.72083                -0.07500                -0.04167  
   ZonaCamana:BLOQUEII   ZonaCastilla:BLOQUEII    ZonaCamana:BLOQUEIII  
               0.05000                 0.17500                 0.07500  
ZonaCastilla:BLOQUEIII  
               0.05000  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                       Value p-value                Decision
Global Stat        5.213e+00  0.2661 Assumptions acceptable.
Skewness           1.568e-32  1.0000 Assumptions acceptable.
Kurtosis           5.102e-01  0.4751 Assumptions acceptable.
Link Function      2.589e+00  0.1076 Assumptions acceptable.
Heteroscedasticity 2.113e+00  0.1460 Assumptions acceptable.

Análisis de varianza

\[Y_{ijk} = \mu + \gamma_k + \tau_{i} + \text{Error}(\tau\text{Bloque})_{i(k)} + \beta_{j} + \epsilon_{ijk}\]

\[\hat{Y}_{ijk} = \mu + \gamma_k + \tau_{i} + \text{Error}(\tau\text{Bloque})_{i(k)} + \beta_{j}\]

Dónde:

\(Y_{ijk}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijk}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor Zona.

\(\text{Error}(\tau\text{Bloque})_{i(k)}\) = Efecto del i-ésimo nivel de Zona en el k-ésimo nivel de repetición.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor tratamiento (Variedad).

\(\gamma_{k}\) = Efecto del k-ésimo nivel del factor Bloque.

\(\epsilon_{ijk}\) = Residuo observado del modelo.

Pruebas de hipótesis

Para el factor A (Zona):

\(H_0: \tau_{A1} = \tau_{A2} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (Variedad):

\(H_0: \beta_{B1} = \beta_{B2} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dbca, test = "F")
Analysis of Variance Table

Response: Diametro_tallo_90dds
            Df   Sum Sq   Mean Sq F value  Pr(>F)  
Zona         1 0.005208 0.0052083  3.0488 0.14123  
VARIEDAD     1 0.005208 0.0052083  3.0488 0.14123  
Zona:BLOQUE  4 0.038333 0.0095833  5.6098 0.04315 *
Residuals    5 0.008542 0.0017083                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
GAD::estimates(modelo.dbca)
$tm
            Zona BLOQUE VARIEDAD        n
Zona           0      3        2 1.714286
VARIEDAD       2      3        0 1.714286
Zona:BLOQUE    1      1        2 1.714286
Res            1      1        1 1.000000

$mse
            Mean square estimates     
Zona        "Res + Zona:BLOQUE + Zona"
VARIEDAD    "Res + VARIEDAD"          
Zona:BLOQUE "Res + Zona:BLOQUE"       
Residual    "Res"                     

$f.versus
            F-ratio versus
Zona        "Zona:BLOQUE" 
VARIEDAD    "Residual"    
Zona:BLOQUE "Residual"    
GAD::gad(modelo.dbca)
Analysis of Variance Table

Response: Diametro_tallo_90dds
            Df   Sum Sq   Mean Sq F value  Pr(>F)  
Zona         1 0.005208 0.0052083  0.5435 0.50190  
VARIEDAD     1 0.005208 0.0052083  3.0488 0.14123  
Zona:BLOQUE  4 0.038333 0.0095833  5.6098 0.04315 *
Residual     5 0.008542 0.0017083                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(Zona/rep)” en el caso de efectos aleatorios o “Error(Zona:rep)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos.

aov(Diametro_tallo_90dds ~ BLOQUE + Zona + VARIEDAD + Error(BLOQUE %in% Zona), data = data_D) -> aov.dbca
summary(aov.dbca)

Error: BLOQUE:Zona
          Df   Sum Sq  Mean Sq F value Pr(>F)
BLOQUE     2 0.025417 0.012708   1.968  0.337
Zona       1 0.005208 0.005208   0.806  0.464
Residuals  2 0.012917 0.006458               

Error: Within
          Df   Sum Sq  Mean Sq F value Pr(>F)
VARIEDAD   1 0.005208 0.005208   3.049  0.141
Residuals  5 0.008542 0.001708               
broom::tidy(aov.dbca)
# A tibble: 5 × 7
  stratum     term         df   sumsq  meansq statistic p.value
  <chr>       <chr>     <dbl>   <dbl>   <dbl>     <dbl>   <dbl>
1 BLOQUE:Zona BLOQUE        2 0.0254  0.0127      1.97    0.337
2 BLOQUE:Zona Zona          1 0.00521 0.00521     0.806   0.464
3 BLOQUE:Zona Residuals     2 0.0129  0.00646    NA      NA    
4 Within      VARIEDAD      1 0.00521 0.00521     3.05    0.141
5 Within      Residuals     5 0.00854 0.00171    NA      NA    
broom::tidy(gad(modelo.dbca))
# A tibble: 4 × 6
  term           df   sumsq  meansq statistic p.value
  <chr>       <int>   <dbl>   <dbl>     <dbl>   <dbl>
1 Zona            1 0.00521 0.00521     0.543  0.502 
2 VARIEDAD        1 0.00521 0.00521     3.05   0.141 
3 Zona:BLOQUE     4 0.0383  0.00958     5.61   0.0432
4 Residual        5 0.00854 0.00171    NA     NA     

Valor de la tabla de F para el factor Zona con una significancia de 0.05.

qf(0.95, 1, 2)
[1] 18.51282

Valor de la tabla de F para el factor Variedad con una significancia de 0.05.

qf(0.95, 1, 5)
[1] 6.607891

Conclusión.

Con respecto al Factor Zona: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor Zona tienen un efecto sobre el diámetro de tallo estadísticamente similar a 0.

Con respecto al Factor Variedad: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor Variedad tienen un efecto sobre el diámetro de tallo estadísticamente similar a 0.

agricolae::cv.model(modelo.dbca)
[1] 5.733918

Comparaciones de medias para los efectos principales del Factor Zona

get_df_ea <- function(object) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  df_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(":", stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(df)
  return(df_rep_A_residuals)
}
get_df_ea(aov.dbca)
[1] 2
get_mse_ea <- function(object) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  meansq_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(":", stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(meansq)
  return(meansq_rep_A_residuals)
}
get_mse_ea(aov.dbca)
[1] 0.006458333
data %>% with(LSD.test(
  Diametro_tallo_90dds, # Cambiar según nombre de variable respuesta
  Zona, # Cambiar según nombre de variable independiente
  DFerror = get_df_ea(aov.dbca), 
  MSerror = get_mse_ea(aov.dbca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: Diametro_tallo_90dds ~ Zona

LSD t Test for Diametro_tallo_90dds 

Mean Square Error:  0.006458333 

Zona,  means and individual ( 95 %) CI

         Diametro_tallo_90dds        std  r       LCL       UCL Min  Max
Camana              0.7270833 0.09205288 24 0.6565018 0.7976648 0.5 0.90
Castilla            0.7395833 0.06753287 24 0.6690018 0.8101648 0.6 0.85

Alpha: 0.05 ; DF Error: 2
Critical Value of t: 4.302653 

least Significant Difference: 0.09981732 

Treatments with the same letter are not significantly different.

         Diametro_tallo_90dds groups
Castilla            0.7395833      a
Camana              0.7270833      a

Comparaciones de medias para los efectos principales del Factor Variedad

data %>% with(LSD.test(
  Diametro_tallo_90dds, # Cambiar según nombre de variable respuesta
  VARIEDAD, # Cambiar según nombre de variable independiente
  DFerror = df.residual(modelo.dbca), 
  MSerror = dvmisc::get_mse(modelo.dbca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: Diametro_tallo_90dds ~ VARIEDAD

LSD t Test for Diametro_tallo_90dds 

Mean Square Error:  0.001708333 

VARIEDAD,  means and individual ( 95 %) CI

  Diametro_tallo_90dds        std  r       LCL      UCL Min  Max
1            0.7583333 0.07322786 24 0.7366457 0.780021 0.6 0.90
2            0.7083333 0.08030738 24 0.6866457 0.730021 0.5 0.85

Alpha: 0.05 ; DF Error: 5
Critical Value of t: 2.570582 

least Significant Difference: 0.03067094 

Treatments with the same letter are not significantly different.

  Diametro_tallo_90dds groups
1            0.7583333      a
2            0.7083333      b

Comparaciones de medias para las interacciones

Para los niveles del factor A dentro del nivel B1:

  • A1 vs A2:

\(H_0: \mu_{A1} - \mu_{A2} = 0\)

\(H_1: \mu_{A1} - \mu_{A2} \neq 0\)

Para los niveles del factor B dentro del nivel A1:

  • B1 vs B2:

\(H_0: \mu_{B1} - \mu_{B2} = 0\)

\(H_1: \mu_{B1} - \mu_{B2} \neq 0\)

NOTA: Repetir este proceso para cada nivel de A y cada nivel de B.

Análisis de varianza para interacción de dos factores con el paquete phia

Comparación de los niveles de B dentro de cada nivel de A

phia::testInteractions(modelo.dbca,
                       fixed = "Zona",
                       across = "VARIEDAD",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
             Value Df Sum of Sq      F Pr(>F)
  Camana  0.041667  1 0.0052083 3.0488 0.1412
Castilla  0.041667  1 0.0052083 3.0488 0.1412
Residuals           5 0.0085417              

Comparación de los niveles de A dentro de cada nivel de B

phia::testInteractions(modelo.dbca,
                       fixed = "VARIEDAD",
                       across = "Zona",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
             Value Df Sum of Sq      F Pr(>F)
1         0.041667  1 0.0052083 3.0488 0.1412
2         0.041667  1 0.0052083 3.0488 0.1412
Residuals           5 0.0085417              

Plot de interacciones

phia::interactionMeans(model = modelo.dbca,
                       factors = c("Zona","VARIEDAD")) %>%
  plot()

Comparaciones de medias de los niveles de B dentro de cada nivel de A

datos_filtrados <- filter_by_2factor_level(data = data,
                       factor_name1 = Zona,
                       factor_name2 =  VARIEDAD)
multcomp.test_2factors <- function(object, respuesta, factor_name1, factor_name2, test, aov){
  
  # Función auxiliar para aplicar la prueba de comparaciones múltiples a un data frame
  multcomp_df <- function(df, respuesta, factor_name, test, aov){
    if (test == "LSD") {
      comp <- LSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "HSD") {
      comp <- HSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "duncan") {
      comp <- duncan.test(df[[respuesta]],
                          df[[factor_name]],
                          DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                          group=TRUE,
                          main = NULL,
                          console=FALSE)[[6]]
    } else if (test == "SNK") {
      comp <- SNK.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[6]]
    } else {
      stop("Test no válido. Los tests disponibles son LSD, HSD, duncan, y SNK.")
    }
    
    return(comp %>%
             rename("y" = "df[[respuesta]]")
           )
  }
  
  # Aplicar la prueba de comparaciones múltiples a todos los data frames dentro de filters1
  comp_filters1 <- lapply(object[[1]], function(df){
    multcomp_df(df, respuesta, factor_name2, test, aov) %>%
      arrange(row.names(.)) %>%
      rownames_to_column(var = "x") %>%
      relocate(x)
  })
  
  # Aplicar la prueba de comparaciones múltiples a todos los data frames dentro de filters2
  comp_filters2 <- lapply(object[[2]], function(df){
    multcomp_df(df, respuesta, factor_name1, test, aov) %>%
      dplyr::arrange(row.names(.)) %>%
      rownames_to_column(var = "x") %>%
      relocate(x) %>%
      dplyr::mutate(groups = toupper(groups))
  })
  
  row.names(comp_filters1) <- NULL
  row.names(comp_filters2) <- NULL
  # Retornar una lista con las comparaciones múltiples para cada data frame
  result <- list()
  result[[as.name(substitute(factor_name1))]] <- comp_filters1
  result[[as.name(substitute(factor_name2))]] <- comp_filters2
  return(#list(#"Comparación de los niveles del factor B dentro de cada nivel del factor A",
         result#[[1]],
         # "Comparación de los niveles del factor A dentro de cada nivel del factor B",
         # result[[2]]
         # )
  )
}
multcomp.test_2factors(
  object = datos_filtrados,
  respuesta = "Diametro_tallo_90dds",
  factor_name1 = "Zona",
  factor_name2 = "VARIEDAD",
  test = "LSD",
  aov = modelo.dbca) -> result.comp
result.comp
$Zona
$Zona$Camana
  x         y groups
1 1 0.7708333      a
2 2 0.6833333      b

$Zona$Castilla
  x         y groups
1 1 0.7458333      a
2 2 0.7333333      a


$VARIEDAD
$VARIEDAD$`1`
         x         y groups
1   Camana 0.7708333      A
2 Castilla 0.7458333      A

$VARIEDAD$`2`
         x         y groups
1   Camana 0.6833333      B
2 Castilla 0.7333333      A
# Convertir la lista a un data frame
df <- result.comp %>%
  reshape2::melt() %>% 
  ungroup() %>%
  dplyr::select(-variable) %>%
  relocate("Factor" = "L1",
           "Nivel" = "L2",
           x,
           "y" = "value",
           groups)
df
    Factor    Nivel        x         y groups
1     Zona   Camana        1 0.7708333      a
2     Zona   Camana        2 0.6833333      b
3     Zona Castilla        1 0.7458333      a
4     Zona Castilla        2 0.7333333      a
5 VARIEDAD        1   Camana 0.7708333      A
6 VARIEDAD        1 Castilla 0.7458333      A
7 VARIEDAD        2   Camana 0.6833333      B
8 VARIEDAD        2 Castilla 0.7333333      A
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # # Convertir level1 y level2 en nombres simbólicos
  # level1 <- as.name(level1)
  # level2 <- as.name(level2)
  # 
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1, level2)) %>%
    dplyr::mutate(groups = paste0(groups.y,groups.x)) %>%
    dplyr::select(!!level1,!!level2, y, groups) #%>%
    # rename(!!level1 := x,
    #        !!level2 := Nivel)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
df2 <- create_report(df = df,
               level1 = "Zona",
               level2 = "VARIEDAD") 
df2 %>% gt()
Zona VARIEDAD y groups
Camana 1 0.7708333 Aa
Camana 2 0.6833333 Bb
Castilla 1 0.7458333 Aa
Castilla 2 0.7333333 Aa
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1,level2)) %>%
    dplyr::mutate(y = paste0(round(y,2), " ", groups.y, groups.x)) %>%
    dplyr::select(!!level1,!!level2, y)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
df3 <- create_report(df = df,
               level1 = "Zona",
               level2 = "VARIEDAD") 
df3 %>% gt()
Zona VARIEDAD y
Camana 1 0.77 Aa
Camana 2 0.68 Bb
Castilla 1 0.75 Aa
Castilla 2 0.73 Aa
df3 %>% 
 pivot_wider(names_from = VARIEDAD,
             values_from = c(y), 
             names_glue = "{VARIEDAD}") %>%
  gt()
Zona 1 2
Camana 0.77 Aa 0.68 Bb
Castilla 0.75 Aa 0.73 Aa

Análisis de DCA de tres vías repetido en el espacio


Definición del modelo


modelo.dca1 <- lm(Diametro_tallo_90dds ~ BLOQUE %in% Zona +
                    DOSIS*VARIEDAD*Zona, data = data)
modelo.dca2 <- lm(Diametro_tallo_90dds ~ BLOQUE %in% Zona +
                    DOSIS+VARIEDAD*Zona, data = data)
modelo.dca3 <- lm(Diametro_tallo_90dds ~ BLOQUE %in% Zona +
                    DOSIS*Zona+VARIEDAD, data = data)
modelo.dca4 <- lm(Diametro_tallo_90dds ~ BLOQUE %in% Zona +
                    DOSIS*VARIEDAD+Zona, data = data)
modelo.dca5 <- lm(Diametro_tallo_90dds ~ BLOQUE %in% Zona +
                    DOSIS+VARIEDAD+Zona, data = data)

Nota

  • La expresión “BLOQUE/ZONA” es para considerar la interacción como efecto fijo.
  • La expresión “BLOQUE:ZONA” es para considerar la interacción como efecto aleatorio.
  • La expresión “BLOQUE %in% ZONA” permite que se genere una estructura del análisis de varianza donde se anide el efecto de la variedad dentro de cada bloque
broom::glance(modelo.dca1) %>%
  bind_rows(broom::glance(modelo.dca2),
            broom::glance(modelo.dca3),
            broom::glance(modelo.dca4),
            broom::glance(modelo.dca5)) %>%
  dplyr::mutate(Modelo = c("Zona * Variedad * Dosis + Bloque/Zona",
                           "Zona * Variedad + Dosis + Bloque/Zona",
                           "Zona * Dosis + Variedad + Bloque/Zona",
                           "Zona + Variedad * Dosis + Bloque/Zona",
                           "Zona + Variedad + Dosis + Bloque/Zona")) %>%
  dplyr::select(Modelo, AIC, BIC) %>%
  dplyr::arrange(BIC) %>%
  dplyr::mutate(Mérito = 1:n()) %>%
  dplyr::relocate(Mérito, Modelo) %>%
  gt()
Mérito Modelo AIC BIC
1 Zona + Variedad + Dosis + Bloque/Zona -95.60372 -75.02051
2 Zona * Variedad + Dosis + Bloque/Zona -97.06583 -74.61142
3 Zona * Dosis + Variedad + Bloque/Zona -92.10054 -65.90372
4 Zona + Variedad * Dosis + Bloque/Zona -90.43563 -64.23882
5 Zona * Variedad * Dosis + Bloque/Zona -97.02292 -57.72770
modelo.dca <- modelo.dca5
summary(modelo.dca)

Call:
lm(formula = Diametro_tallo_90dds ~ BLOQUE %in% Zona + DOSIS + 
    VARIEDAD + Zona, data = data)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.191667 -0.043229 -0.005208  0.052083  0.152083 

Coefficients:
                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)             7.375e-01  3.646e-02  20.226   <2e-16 ***
DOSIS1                  1.667e-02  3.261e-02   0.511   0.6123    
DOSIS2                  1.667e-02  3.261e-02   0.511   0.6123    
DOSIS3                  1.667e-02  3.261e-02   0.511   0.6123    
VARIEDAD2              -5.000e-02  2.306e-02  -2.168   0.0365 *  
ZonaCastilla           -6.250e-03  3.994e-02  -0.156   0.8765    
BLOQUEII:ZonaCamana    -1.250e-02  3.994e-02  -0.313   0.7560    
BLOQUEIII:ZonaCamana    1.875e-02  3.994e-02   0.469   0.6414    
BLOQUEII:ZonaCastilla   6.250e-02  3.994e-02   1.565   0.1259    
BLOQUEIII:ZonaCastilla -2.602e-18  3.994e-02   0.000   1.0000    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.07988 on 38 degrees of freedom
Multiple R-squared:  0.1961,    Adjusted R-squared:  0.005743 
F-statistic:  1.03 on 9 and 38 DF,  p-value: 0.4346

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dca)
ggResidpanel::resid_panel(modelo.dca)
influence.measures(modelo.dca)
Influence measures of
     lm(formula = Diametro_tallo_90dds ~ BLOQUE %in% Zona + DOSIS +      VARIEDAD + Zona, data = data) :

      dfb.1_ dfb.DOSIS1 dfb.DOSIS2 dfb.DOSIS3 dfb.VARI  dfb.ZnCs
1   8.91e-02  -3.98e-02  -3.98e-02  -3.98e-02 -0.02816 -4.88e-02
2   2.17e-01  -2.42e-01  -2.42e-01  -2.42e-01 -0.17144 -6.66e-16
3  -1.78e-02   1.99e-02   1.99e-02   1.99e-02  0.01408 -2.11e-17
4  -2.14e-01   1.20e-01   1.20e-01   1.20e-01 -0.08476  1.47e-01
5   3.57e-02  -7.98e-02  -7.98e-02  -7.98e-02  0.05639  1.25e-17
6   1.37e-01  -3.06e-01  -3.06e-01  -3.06e-01  0.21614  1.08e-16
7  -2.33e-01  -1.74e-01  -5.35e-17  -5.42e-17  0.12293  2.13e-01
8  -1.77e-16   1.87e-01  -1.67e-17  -2.12e-18 -0.13255  2.06e-16
9   1.49e-17   8.64e-02  -2.95e-17  -3.92e-18 -0.06111 -4.07e-17
10 -1.19e-02  -1.33e-02  -4.83e-18  -3.53e-18 -0.00938  1.63e-02
11  1.34e-01  -2.99e-01   9.92e-18   1.69e-17 -0.21111 -1.88e-16
12  3.27e-02  -7.31e-02   2.09e-17   6.63e-18 -0.05168  2.87e-18
13 -1.78e-02  -1.55e-17  -1.33e-02  -4.59e-18  0.00938  1.63e-02
14 -1.52e-16  -1.14e-16   1.87e-01   4.25e-18 -0.13255  1.32e-16
15  2.39e-16  -3.33e-17  -5.99e-01   6.79e-18  0.42382 -1.88e-16
16 -1.19e-02  -1.55e-17  -1.33e-02  -3.98e-18 -0.00938  1.63e-02
17 -1.59e-01  -2.37e-16   3.56e-01  -8.07e-18  0.25179  2.52e-16
18  3.27e-02  -4.06e-18  -7.31e-02   4.14e-18 -0.05168 -2.58e-17
19  6.61e-01   6.34e-16   2.61e-16   4.93e-01 -0.34828 -6.03e-01
20  1.65e-16   8.14e-17   0.00e+00  -1.33e-01  0.09426 -1.36e-16
21 -5.35e-17   1.38e-17  -9.96e-17   4.23e-01 -0.29906  0.00e+00
22 -1.55e-01  -2.21e-16  -1.13e-16  -1.74e-01 -0.12293  2.13e-01
23  3.04e-01   4.26e-16  -7.99e-17  -6.79e-01 -0.48001 -6.40e-16
24  3.27e-02  -5.25e-18   8.61e-18  -7.31e-02 -0.05168 -1.72e-17
25 -2.36e-01   2.63e-01   2.63e-01   2.63e-01  0.18621 -3.23e-01
26  1.78e-02  -1.99e-02  -1.99e-02  -1.99e-02 -0.01408 -4.53e-18
27 -8.92e-02   9.98e-02   9.98e-02   9.98e-02  0.07056  3.08e-17
28 -1.18e-01   2.63e-01   2.63e-01   2.63e-01 -0.18621 -3.23e-01
29  8.08e-02  -1.81e-01  -1.81e-01  -1.81e-01  0.12774  3.68e-17
30 -4.46e-02   9.98e-02   9.98e-02   9.98e-02 -0.07056 -4.35e-18
31 -8.62e-17   1.67e-01   3.19e-17   8.05e-18 -0.11813  2.05e-01
32  5.71e-18  -3.32e-02   8.05e-20  -2.44e-18  0.02347 -1.18e-17
33  2.64e-17  -1.54e-01  -1.24e-18  -1.00e-17  0.10856 -5.40e-17
34 -2.97e-03   6.64e-03   1.64e-18   1.88e-20  0.00469  8.13e-03
35  1.48e-02  -3.32e-02  -1.77e-18  -9.40e-19 -0.02347 -1.34e-17
36 -1.50e-01   3.34e-01   2.14e-17   6.63e-18  0.23640  1.47e-16
37 -5.03e-17   0.00e+00   1.67e-01   1.37e-17 -0.11813  2.05e-01
38  4.90e-17  -3.24e-17  -1.94e-01  -2.09e-17  0.13737 -4.31e-17
39 -4.21e-17   2.78e-17   1.67e-01   1.66e-17 -0.11813  3.00e-17
40 -2.97e-03  -1.10e-18   6.64e-03   2.44e-19  0.00469  8.13e-03
41 -5.66e-02   7.03e-18   1.27e-01   7.89e-18  0.08951  5.22e-17
42  6.87e-02  -8.52e-18  -1.54e-01  -8.26e-18 -0.10856 -5.08e-17
43  1.26e-16  -1.99e-17  -1.13e-16  -3.20e-01  0.22624 -3.92e-01
44  8.28e-18  -5.64e-18  -5.86e-18  -3.32e-02  0.02347 -3.68e-18
45  4.02e-17  -3.46e-17  -2.71e-17  -1.54e-01  0.10856  1.36e-17
46 -2.31e-01  -4.92e-18   2.43e-16   5.16e-01  0.36521  6.33e-01
47  1.48e-02  -6.94e-18  -9.77e-18  -3.32e-02 -0.02347 -1.31e-17
48 -7.47e-02   3.49e-17   4.92e-17   1.67e-01  0.11813  7.20e-17
   dfb.BLOQUEII.ZnCm dfb.BLOQUEIII.ZnCm dfb.BLOQUEII.ZnCs dfb.BLOQUEIII.ZnCs
1          -4.88e-02          -4.88e-02         -4.47e-17          -3.79e-17
2           2.97e-01          -5.44e-16          1.03e-16           1.60e-16
3          -1.17e-17          -2.44e-02          1.61e-17           1.83e-17
4           1.47e-01           1.47e-01         -3.59e-18          -1.56e-17
5           9.77e-02           2.17e-17          5.79e-18           1.60e-17
6           3.60e-17           3.74e-01          6.63e-17           6.36e-17
7           2.13e-01           2.13e-01         -2.27e-17          -2.82e-17
8           2.30e-01           2.17e-16         -4.57e-17          -8.61e-17
9           0.00e+00           1.06e-01          2.93e-17           7.53e-17
10          1.63e-02           1.63e-02          8.03e-20           2.48e-18
11         -3.66e-01          -2.03e-16          2.03e-17           1.29e-17
12          8.61e-18          -8.95e-02         -6.13e-18          -2.63e-18
13          1.63e-02           1.63e-02         -2.67e-18          -3.79e-18
14          2.30e-01           9.56e-17         -1.83e-17          -8.25e-18
15         -1.41e-16          -7.34e-01         -3.26e-17          -2.11e-17
16          1.63e-02           1.63e-02         -2.50e-18          -3.91e-18
17          4.36e-01           1.57e-16         -3.91e-17          -1.25e-17
18         -8.61e-18          -8.95e-02         -3.07e-18          -3.23e-18
19         -6.03e-01          -6.03e-01          9.25e-17           1.21e-16
20         -1.63e-01          -1.13e-16          1.48e-17           1.13e-17
21          0.00e+00           5.18e-01          1.74e-17          -2.37e-18
22          2.13e-01           2.13e-01         -1.87e-17          -3.82e-17
23         -8.31e-01          -4.62e-16          1.30e-16           7.46e-17
24          0.00e+00          -8.95e-02          2.87e-18           2.24e-18
25         -4.49e-17           2.26e-17          3.23e-01           3.23e-01
26         -1.11e-18          -3.10e-18          2.44e-02           5.92e-18
27          5.37e-18           1.66e-17         -2.35e-17          -1.22e-01
28         -3.95e-17          -1.32e-17          3.23e-01           3.23e-01
29         -1.37e-17          -3.52e-18          2.21e-01          -1.28e-17
30          7.40e-18           3.05e-18          0.00e+00          -1.22e-01
31          6.67e-17           4.24e-17         -2.05e-01          -2.05e-01
32         -5.75e-18          -6.12e-18         -4.06e-02           4.54e-18
33         -2.69e-17          -2.66e-17          3.62e-17          -1.88e-01
34          2.71e-18           2.59e-18         -8.13e-03          -8.13e-03
35         -6.05e-18          -1.06e-17         -4.06e-02           3.23e-18
36          6.16e-17           1.03e-16         -3.94e-17           4.09e-01
37          2.32e-17          -2.00e-17         -2.05e-01          -2.05e-01
38          1.70e-17           3.68e-17         -2.38e-01           6.43e-18
39         -1.43e-17          -3.35e-17         -1.97e-17           2.05e-01
40         -4.16e-19          -3.44e-19         -8.13e-03          -8.13e-03
41         -3.66e-17          -1.54e-17          1.55e-01          -1.64e-17
42          4.41e-17           2.04e-17          3.62e-17          -1.88e-01
43         -5.60e-17           5.72e-18          3.92e-01           3.92e-01
44          1.70e-18           2.90e-18         -4.06e-02           1.25e-18
45          7.57e-18           1.51e-17         -1.81e-17          -1.88e-01
46          9.51e-17           6.10e-17         -6.33e-01          -6.33e-01
47          1.39e-18          -1.61e-18         -4.06e-02           4.45e-18
48         -6.71e-18           6.24e-18         -5.90e-17           2.05e-01
     dffit cov.r   cook.d   hat inf
1   0.0891 1.636 8.14e-04 0.208    
2   0.5421 1.225 2.93e-02 0.208    
3  -0.0445 1.646 2.03e-04 0.208    
4  -0.2680 1.532 7.33e-03 0.208    
5   0.1783 1.596 3.26e-03 0.208    
6   0.6835 1.032 4.58e-02 0.208    
7  -0.3887 1.414 1.53e-02 0.208    
8   0.4192 1.379 1.77e-02 0.208    
9   0.1932 1.587 3.82e-03 0.208    
10 -0.0297 1.648 9.04e-05 0.208    
11 -0.6676 1.054 4.38e-02 0.208    
12 -0.1634 1.605 2.74e-03 0.208    
13 -0.0297 1.648 9.04e-05 0.208    
14  0.4192 1.379 1.77e-02 0.208    
15 -1.3402 0.303 1.56e-01 0.208    
16 -0.0297 1.648 9.04e-05 0.208    
17  0.7962 0.878 6.11e-02 0.208    
18 -0.1634 1.605 2.74e-03 0.208    
19  1.1014 0.510 1.11e-01 0.208    
20 -0.2981 1.506 9.04e-03 0.208    
21  0.9457 0.685 8.41e-02 0.208    
22 -0.3887 1.414 1.53e-02 0.208    
23 -1.5179 0.197 1.91e-01 0.208   *
24 -0.1634 1.605 2.74e-03 0.208    
25 -0.5888 1.162 3.44e-02 0.208    
26  0.0445 1.646 2.03e-04 0.208    
27 -0.2231 1.567 5.09e-03 0.208    
28 -0.5888 1.162 3.44e-02 0.208    
29  0.4039 1.397 1.65e-02 0.208    
30 -0.2231 1.567 5.09e-03 0.208    
31  0.3736 1.430 1.41e-02 0.208    
32 -0.0742 1.640 5.65e-04 0.208    
33 -0.3433 1.462 1.20e-02 0.208    
34  0.0148 1.649 2.26e-05 0.208    
35 -0.0742 1.640 5.65e-04 0.208    
36  0.7476 0.944 5.43e-02 0.208    
37  0.3736 1.430 1.41e-02 0.208    
38 -0.4344 1.361 1.90e-02 0.208    
39  0.3736 1.430 1.41e-02 0.208    
40  0.0148 1.649 2.26e-05 0.208    
41  0.2831 1.519 8.16e-03 0.208    
42 -0.3433 1.462 1.20e-02 0.208    
43 -0.7154 0.988 4.99e-02 0.208    
44 -0.0742 1.640 5.65e-04 0.208    
45 -0.3433 1.462 1.20e-02 0.208    
46  1.1549 0.457 1.20e-01 0.208    
47 -0.0742 1.640 5.65e-04 0.208    
48  0.3736 1.430 1.41e-02 0.208    
influenceIndexPlot(modelo.dca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1     -0.13534507      2.258860  0.6032
   2      0.05958262      1.845361  0.6444
   3     -0.04655284      1.962092  0.4828
   4     -0.15821879      2.170157  0.2696
   5      0.17470289      1.501289  0.3276
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dca
DW = 2.2589, p-value = 0.6066
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.dca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dca)
W = 0.96809, p-value = 0.2132
ad.test(rstudent(modelo.dca))

    Anderson-Darling normality test

data:  rstudent(modelo.dca)
A = 0.51434, p-value = 0.1832
lillie.test(rstudent(modelo.dca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dca)
D = 0.092111, p-value = 0.3907
ks.test(rstudent(modelo.dca), "pnorm",
        alternative = "two.sided")

    Asymptotic one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dca)
D = 0.09263, p-value = 0.8047
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dca)
W = 0.079806, p-value = 0.2033
pearson.test(rstudent(modelo.dca))

    Pearson chi-square normality test

data:  rstudent(modelo.dca)
P = 10.333, p-value = 0.1705
sf.test(rstudent(modelo.dca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dca)
W = 0.96394, p-value = 0.1295

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 0.7436697, Df = 1, p = 0.38849
bptest(modelo.dca)

    studentized Breusch-Pagan test

data:  modelo.dca
BP = 11.834, df = 9, p-value = 0.2228
bptest(modelo.dca, studentize = F)

    Breusch-Pagan test

data:  modelo.dca
BP = 14.449, df = 9, p-value = 0.1072
olsrr::ols_test_breusch_pagan(modelo.dca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

                      Data                       
 ------------------------------------------------
 Response : Diametro_tallo_90dds 
 Variables: fitted values of Diametro_tallo_90dds 

        Test Summary         
 ----------------------------
 DF            =    1 
 Chi2          =    0.7436697 
 Prob > Chi2   =    0.3884879 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dca %>% gvlma()

Call:
lm(formula = Diametro_tallo_90dds ~ BLOQUE %in% Zona + DOSIS + 
    VARIEDAD + Zona, data = data)

Coefficients:
           (Intercept)                  DOSIS1                  DOSIS2  
             7.375e-01               1.667e-02               1.667e-02  
                DOSIS3               VARIEDAD2            ZonaCastilla  
             1.667e-02              -5.000e-02              -6.250e-03  
   BLOQUEII:ZonaCamana    BLOQUEIII:ZonaCamana   BLOQUEII:ZonaCastilla  
            -1.250e-02               1.875e-02               6.250e-02  
BLOQUEIII:ZonaCastilla  
            -2.602e-18  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                      Value p-value                Decision
Global Stat        1.804587  0.7716 Assumptions acceptable.
Skewness           0.181520  0.6701 Assumptions acceptable.
Kurtosis           0.390464  0.5321 Assumptions acceptable.
Link Function      1.228629  0.2677 Assumptions acceptable.
Heteroscedasticity 0.003974  0.9497 Assumptions acceptable.

Análisis de varianza

\[Y_{ijkl} = \mu + \tau_{i} + \text{Error}(\tau\text{rep})_{i(l)} + \beta_{j} + \gamma_{k} + \epsilon_{ijkl}\]

\[\hat{Y}_{ijkl} = \mu + \tau_{i} + \text{Error}(\tau\text{rep})_{i(l)} + \beta_{j} + \gamma_{k}\]

Dónde:

\(Y_{ijkl}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijkl}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor Zona.

\(\text{Error}(\tau\text{rep})_{i(k)}\) = Efecto del i-ésimo nivel de Zona en el k-ésimo nivel de repetición.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor tratamiento (Variedad).

\(\gamma_{k}\) = Efecto del k-ésimo nivel del factor tratamiento (Dosis).

\(\epsilon_{ijkl}\) = Residuo observado del modelo.

Pruebas de hipótesis

Para el factor A (Zona):

\(H_0: \tau_{A1} = \tau_{A2} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (Variedad):

\(H_0: \beta_{B1} = \beta_{B2} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Para el factor C (Dosis):

\(H_0: \gamma_{C1} = \gamma_{C2} = 0\)

\(H_1: \text{En al menos un nivel del factor C el } \beta \text{ es diferente a los demás.}\)

\(H_1: \gamma_k \neq 0\text{; en al menos un nivel del factor C.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dca, test = "F")
Analysis of Variance Table

Response: Diametro_tallo_90dds
            Df   Sum Sq   Mean Sq F value  Pr(>F)  
DOSIS        3 0.002500 0.0008333  0.1306 0.94131  
VARIEDAD     1 0.030000 0.0300000  4.7010 0.03647 *
Zona         1 0.001875 0.0018750  0.2938 0.59095  
BLOQUE:Zona  4 0.024792 0.0061979  0.9712 0.43458  
Residuals   38 0.242500 0.0063816                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
GAD::estimates(modelo.dca)
$tm
            BLOQUE Zona DOSIS VARIEDAD   n
DOSIS            3    2     0        2 4.8
VARIEDAD         3    2     4        0 4.8
Zona             3    0     4        2 4.8
BLOQUE:Zona      1    1     4        2 4.8
Res              1    1     1        1 1.0

$mse
            Mean square estimates     
DOSIS       "Res + DOSIS"             
VARIEDAD    "Res + VARIEDAD"          
Zona        "Res + BLOQUE:Zona + Zona"
BLOQUE:Zona "Res + BLOQUE:Zona"       
Residual    "Res"                     

$f.versus
            F-ratio versus
DOSIS       "Residual"    
VARIEDAD    "Residual"    
Zona        "BLOQUE:Zona" 
BLOQUE:Zona "Residual"    
GAD::gad(modelo.dca)
Analysis of Variance Table

Response: Diametro_tallo_90dds
            Df   Sum Sq   Mean Sq F value  Pr(>F)  
DOSIS        3 0.002500 0.0008333  0.1306 0.94131  
VARIEDAD     1 0.030000 0.0300000  4.7010 0.03647 *
Zona         1 0.001875 0.0018750  0.3025 0.61157  
BLOQUE:Zona  4 0.024792 0.0061979  0.9712 0.43458  
Residual    38 0.242500 0.0063816                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(Zona/rep)” en el caso de efectos aleatorios o “Error(Zona:rep)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos.

aov(Diametro_tallo_90dds ~ Zona + VARIEDAD + DOSIS + Error(BLOQUE %in% Zona), data = data) -> aov.dca
summary(aov.dca)

Error: BLOQUE:Zona
          Df   Sum Sq  Mean Sq F value Pr(>F)
Zona       1 0.001875 0.001875   0.303  0.612
Residuals  4 0.024792 0.006198               

Error: Within
          Df Sum Sq  Mean Sq F value Pr(>F)  
VARIEDAD   1 0.0300 0.030000   4.701 0.0365 *
DOSIS      3 0.0025 0.000833   0.131 0.9413  
Residuals 38 0.2425 0.006382                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
broom::tidy(aov.dca)
# A tibble: 5 × 7
  stratum     term         df   sumsq   meansq statistic p.value
  <chr>       <chr>     <dbl>   <dbl>    <dbl>     <dbl>   <dbl>
1 BLOQUE:Zona Zona          1 0.00187 0.00187      0.303  0.612 
2 BLOQUE:Zona Residuals     4 0.0248  0.00620     NA     NA     
3 Within      VARIEDAD      1 0.0300  0.0300       4.70   0.0365
4 Within      DOSIS         3 0.00250 0.000833     0.131  0.941 
5 Within      Residuals    38 0.243   0.00638     NA     NA     
broom::tidy(gad(modelo.dca))
# A tibble: 5 × 6
  term           df   sumsq   meansq statistic p.value
  <chr>       <int>   <dbl>    <dbl>     <dbl>   <dbl>
1 DOSIS           3 0.00250 0.000833     0.131  0.941 
2 VARIEDAD        1 0.0300  0.0300       4.70   0.0365
3 Zona            1 0.00187 0.00187      0.303  0.612 
4 BLOQUE:Zona     4 0.0248  0.00620      0.971  0.435 
5 Residual       38 0.243   0.00638     NA     NA     

Valor de la tabla de F para el factor Zona con una significancia de 0.05.

qf(0.95, 1, 4)
[1] 7.708647

Valor de la tabla de F para el factor Variedad con una significancia de 0.05.

qf(0.95, 1, 38)
[1] 4.098172

Valor de la tabla de F para el factor Dosis con una significancia de 0.05.

qf(0.95, 3, 38)
[1] 2.851741

Conclusión.

Con respecto al Factor Zona: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor Zona tienen un efecto sobre el diámetro de tallo estadísticamente similar a 0.

Con respecto al Factor Variedad: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor Variedad tienen un efecto sobre el diámetro de tallo estadísticamente diferente a 0.

Con respecto al Factor Dosis: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor Dosis tienen un efecto sobre el diámetro de tallo estadísticamente similar a 0.

agricolae::cv.model(modelo.dca)
[1] 10.89338

Comparaciones de medias para los efectos principales del Factor Zona

get_df_ea <- function(object) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  df_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(":", stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(df)
  return(df_rep_A_residuals)
}
get_df_ea(aov.dca)
[1] 4
get_mse_ea <- function(object) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  meansq_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(":", stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(meansq)
  return(meansq_rep_A_residuals)
}
get_mse_ea(aov.dca)
[1] 0.006197917
data %>% with(LSD.test(
  Diametro_tallo_90dds, # Cambiar según nombre de variable respuesta
  Zona, # Cambiar según nombre de variable independiente
  DFerror = get_df_ea(aov.dca), 
  MSerror = get_mse_ea(aov.dca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: Diametro_tallo_90dds ~ Zona

LSD t Test for Diametro_tallo_90dds 

Mean Square Error:  0.006197917 

Zona,  means and individual ( 95 %) CI

         Diametro_tallo_90dds        std  r       LCL       UCL Min  Max
Camana              0.7270833 0.09205288 24 0.6824657 0.7717009 0.5 0.90
Castilla            0.7395833 0.06753287 24 0.6949657 0.7842009 0.6 0.85

Alpha: 0.05 ; DF Error: 4
Critical Value of t: 2.776445 

least Significant Difference: 0.06309883 

Treatments with the same letter are not significantly different.

         Diametro_tallo_90dds groups
Castilla            0.7395833      a
Camana              0.7270833      a

Comparaciones de medias para los efectos principales del Factor Variedad

data %>% with(LSD.test(
  Diametro_tallo_90dds, # Cambiar según nombre de variable respuesta
  VARIEDAD, # Cambiar según nombre de variable independiente
  DFerror = df.residual(modelo.dca), 
  MSerror = dvmisc::get_mse(modelo.dca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: Diametro_tallo_90dds ~ VARIEDAD

LSD t Test for Diametro_tallo_90dds 

Mean Square Error:  0.006381579 

VARIEDAD,  means and individual ( 95 %) CI

  Diametro_tallo_90dds        std  r       LCL       UCL Min  Max
1            0.7583333 0.07322786 24 0.7253227 0.7913439 0.6 0.90
2            0.7083333 0.08030738 24 0.6753227 0.7413439 0.5 0.85

Alpha: 0.05 ; DF Error: 38
Critical Value of t: 2.024394 

least Significant Difference: 0.04668405 

Treatments with the same letter are not significantly different.

  Diametro_tallo_90dds groups
1            0.7583333      a
2            0.7083333      b

Comparaciones de medias para los efectos principales del Factor Dosis

data %>% with(LSD.test(
  Diametro_tallo_90dds, # Cambiar según nombre de variable respuesta
  DOSIS, # Cambiar según nombre de variable independiente
  DFerror = df.residual(modelo.dca), 
  MSerror = dvmisc::get_mse(modelo.dca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: Diametro_tallo_90dds ~ DOSIS

LSD t Test for Diametro_tallo_90dds 

Mean Square Error:  0.006381579 

DOSIS,  means and individual ( 95 %) CI

  Diametro_tallo_90dds        std  r       LCL       UCL Min Max
0            0.7208333 0.07216878 12 0.6741493 0.7675174 0.6 0.8
1            0.7375000 0.06440285 12 0.6908159 0.7841841 0.6 0.8
2            0.7375000 0.06784005 12 0.6908159 0.7841841 0.6 0.8
3            0.7375000 0.11505927 12 0.6908159 0.7841841 0.5 0.9

Alpha: 0.05 ; DF Error: 38
Critical Value of t: 2.024394 

least Significant Difference: 0.06602122 

Treatments with the same letter are not significantly different.

  Diametro_tallo_90dds groups
1            0.7375000      a
2            0.7375000      a
3            0.7375000      a
0            0.7208333      a

Análisis de DBCA de tres vías repetido en el espacio


Definición del modelo


modelo.dbca1 <- lm(Diametro_tallo_90dds ~ BLOQUE + BLOQUE %in% Zona +
                    DOSIS*VARIEDAD*Zona, data = data)
modelo.dbca2 <- lm(Diametro_tallo_90dds ~ BLOQUE + BLOQUE %in% Zona +
                    DOSIS+VARIEDAD*Zona, data = data)
modelo.dbca3 <- lm(Diametro_tallo_90dds ~ BLOQUE + BLOQUE %in% Zona +
                    DOSIS*Zona+VARIEDAD, data = data)
modelo.dbca4 <- lm(Diametro_tallo_90dds ~ BLOQUE + BLOQUE %in% Zona +
                    DOSIS*VARIEDAD+Zona, data = data)
modelo.dbca5 <- lm(Diametro_tallo_90dds ~ BLOQUE + BLOQUE %in% Zona +
                    DOSIS+VARIEDAD+Zona, data = data)

Nota

  • La expresión “BLOQUE/ZONA” es para considerar la interacción como efecto fijo.
  • La expresión “BLOQUE:ZONA” es para considerar la interacción como efecto aleatorio.
  • La expresión “BLOQUE %in% ZONA” permite que se genere una estructura del análisis de varianza donde se anide el efecto de la variedad dentro de cada bloque
broom::glance(modelo.dbca1) %>%
  bind_rows(broom::glance(modelo.dbca2),
            broom::glance(modelo.dbca3),
            broom::glance(modelo.dbca4),
            broom::glance(modelo.dbca5)) %>%
  dplyr::mutate(Modelo = c("Bloque + Zona * Variedad * Dosis + Bloque/Zona",
                           "Bloque + Zona * Variedad + Dosis + Bloque/Zona",
                           "Bloque + Zona * Dosis + Variedad + Bloque/Zona",
                           "Bloque + Zona + Variedad * Dosis + Bloque/Zona",
                           "Bloque + Zona + Variedad + Dosis + Bloque/Zona")) %>%
  dplyr::select(Modelo, AIC, BIC) %>%
  dplyr::arrange(BIC) %>%
  dplyr::mutate(Mérito = 1:n()) %>%
  dplyr::relocate(Mérito, Modelo) %>%
  gt()
Mérito Modelo AIC BIC
1 Bloque + Zona + Variedad + Dosis + Bloque/Zona -95.60372 -75.02051
2 Bloque + Zona * Variedad + Dosis + Bloque/Zona -97.06583 -74.61142
3 Bloque + Zona * Dosis + Variedad + Bloque/Zona -92.10054 -65.90372
4 Bloque + Zona + Variedad * Dosis + Bloque/Zona -90.43563 -64.23882
5 Bloque + Zona * Variedad * Dosis + Bloque/Zona -97.02292 -57.72770
modelo.dbca <- modelo.dbca1
summary(modelo.dbca)

Call:
lm(formula = Diametro_tallo_90dds ~ BLOQUE + BLOQUE %in% Zona + 
    DOSIS * VARIEDAD * Zona, data = data)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.133333 -0.045833  0.004167  0.043229  0.097917 

Coefficients:
                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                    7.646e-01  4.806e-02  15.909 1.48e-15 ***
BLOQUEII                      -1.250e-02  3.723e-02  -0.336   0.7395    
BLOQUEIII                      1.875e-02  3.723e-02   0.504   0.6184    
DOSIS1                        -1.381e-15  6.079e-02   0.000   1.0000    
DOSIS2                        -5.000e-02  6.079e-02  -0.823   0.4177    
DOSIS3                         6.667e-02  6.079e-02   1.097   0.2821    
VARIEDAD2                     -5.000e-02  6.079e-02  -0.823   0.4177    
ZonaCastilla                  -6.875e-02  6.797e-02  -1.012   0.3204    
BLOQUEII:ZonaCastilla          7.500e-02  5.265e-02   1.425   0.1653    
BLOQUEIII:ZonaCastilla        -1.875e-02  5.265e-02  -0.356   0.7244    
DOSIS1:VARIEDAD2              -5.000e-02  8.597e-02  -0.582   0.5655    
DOSIS2:VARIEDAD2               6.667e-02  8.597e-02   0.775   0.4446    
DOSIS3:VARIEDAD2              -1.667e-01  8.597e-02  -1.939   0.0627 .  
ZonaCastilla:DOSIS1            5.000e-02  8.597e-02   0.582   0.5655    
ZonaCastilla:DOSIS2            1.167e-01  8.597e-02   1.357   0.1856    
ZonaCastilla:DOSIS3           -6.667e-02  8.597e-02  -0.775   0.4446    
ZonaCastilla:VARIEDAD2         1.667e-02  8.597e-02   0.194   0.8477    
ZonaCastilla:DOSIS1:VARIEDAD2  6.667e-02  1.216e-01   0.548   0.5878    
ZonaCastilla:DOSIS2:VARIEDAD2 -1.000e-01  1.216e-01  -0.823   0.4177    
ZonaCastilla:DOSIS3:VARIEDAD2  2.667e-01  1.216e-01   2.193   0.0368 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.07445 on 28 degrees of freedom
Multiple R-squared:  0.4855,    Adjusted R-squared:  0.1364 
F-statistic: 1.391 on 19 and 28 DF,  p-value: 0.2091

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dbca)
ggResidpanel::resid_panel(modelo.dbca)
influence.measures(modelo.dbca)
Influence measures of
     lm(formula = Diametro_tallo_90dds ~ BLOQUE + BLOQUE %in% Zona +      DOSIS * VARIEDAD * Zona, data = data) :

      dfb.1_ dfb.BLOQUEII dfb.BLOQUEIII dfb.DOSIS1 dfb.DOSIS2 dfb.DOSIS3
1  -2.13e-01     8.25e-02      8.25e-02   1.35e-01   1.35e-01   1.35e-01
2   4.96e-01     2.74e-01     -1.01e-15  -4.48e-01  -4.48e-01  -4.48e-01
3  -3.43e-01     2.32e-16     -1.90e-01   3.10e-01   3.10e-01   3.10e-01
4  -1.93e-01     3.74e-01      3.74e-01   3.51e-16   2.95e-16   9.16e-18
5   3.04e-03    -1.18e-02     -1.18e-17  -2.74e-18   2.40e-17   2.27e-19
6  -9.98e-02     3.42e-16      3.86e-01   3.96e-16   2.01e-16   5.39e-16
7  -1.93e-01     3.74e-01      3.74e-01  -6.10e-01  -9.89e-17  -3.28e-17
8  -7.08e-02     2.74e-01      9.94e-17   4.48e-01   4.93e-17  -8.87e-17
9  -2.44e-02     7.70e-17      9.44e-02   1.54e-01   1.05e-17   4.85e-17
10  1.04e-01    -2.02e-01     -2.02e-01  -2.64e-16  -1.33e-16  -1.26e-16
11  7.72e-02    -2.99e-01     -1.08e-16  -2.91e-16  -1.27e-16  -1.13e-16
12 -2.44e-02     4.49e-17      9.44e-02  -6.97e-17   4.40e-17  -2.01e-17
13  1.04e-01    -2.02e-01     -2.02e-01  -2.19e-16   3.29e-01  -1.07e-16
14 -1.51e-01     5.85e-01      3.58e-16   3.18e-16   9.56e-01   2.33e-16
15  2.17e-01    -8.00e-16     -8.41e-01  -4.57e-16  -1.37e+00  -5.25e-16
16 -9.17e-02     1.78e-01      1.78e-01   2.10e-16   9.93e-17   2.30e-16
17 -1.23e-01     4.77e-01      3.23e-16   6.77e-16   1.21e-15   5.90e-16
18  7.40e-02    -1.17e-16     -2.87e-01   3.59e-18  -1.71e-18   5.98e-18
19  2.06e-01    -3.99e-01     -3.99e-01  -5.07e-16  -6.52e-16   6.52e-01
20  1.89e-01    -7.31e-01     -4.51e-16  -6.98e-16  -7.02e-16  -1.19e+00
21 -7.40e-02     1.36e-16      2.87e-01   2.44e-17  -8.27e-17   4.68e-01
22  1.04e-01    -2.02e-01     -2.02e-01  -2.00e-16  -1.59e-16  -2.37e-16
23  1.58e-01    -6.13e-01     -3.63e-16  -4.65e-16  -4.75e-16  -3.70e-16
24 -9.98e-02     1.84e-16      3.86e-01   1.36e-17  -9.16e-17  -1.22e-16
25 -1.58e-16    -1.02e-16     -1.46e-16  -8.83e-17   2.20e-16   9.98e-17
26  8.20e-17     1.10e-16      5.23e-17  -1.33e-17  -2.78e-16  -1.31e-16
27  3.73e-18     1.29e-17      7.70e-18   4.94e-18  -1.90e-17  -8.38e-18
28  2.81e-16    -4.70e-17     -7.77e-17  -1.87e-16  -3.37e-16  -2.04e-16
29 -1.76e-17    -7.24e-18     -6.41e-17  -5.88e-17   1.32e-16  -9.48e-17
30  7.53e-17    -1.83e-17     -4.63e-18  -5.79e-17  -8.17e-17  -6.14e-17
31 -1.29e-16     2.83e-17      4.25e-17  -1.65e-17   5.96e-18   2.57e-17
32  2.18e-17    -2.81e-18      6.13e-18  -1.16e-17  -8.06e-18  -6.92e-18
33 -2.19e-16    -2.20e-17      3.43e-18   3.97e-16   2.14e-16   2.21e-16
34  1.39e-16    -2.63e-17     -2.26e-17  -1.60e-16  -7.13e-17  -1.05e-16
35 -1.12e-16     6.10e-18      6.81e-18   6.38e-17   1.45e-16   1.57e-16
36  1.34e-16     9.72e-17      9.16e-17  -3.01e-16  -2.13e-16  -2.51e-16
37 -8.22e-17     1.10e-17      1.24e-17   5.79e-17   9.90e-17   3.35e-17
38  1.96e-16    -6.27e-18     -8.20e-17  -4.02e-17  -3.26e-16   2.18e-17
39 -7.21e-17     1.91e-17      1.40e-17   7.28e-17   1.81e-16   3.27e-18
40 -3.93e-18    -1.06e-18      3.22e-18   5.91e-18  -6.32e-18   5.08e-18
41  6.26e-17     2.10e-17      1.50e-17  -1.03e-16  -2.50e-17  -5.39e-17
42 -1.10e-16    -3.10e-17      3.43e-18   5.35e-17   1.80e-16   7.51e-17
43  1.55e-16     2.21e-17     -1.52e-17  -1.34e-16  -1.73e-16  -1.36e-16
44 -5.13e-17     2.80e-17      2.90e-17  -5.44e-17   3.03e-17   3.02e-17
45 -3.74e-18     5.43e-18      3.39e-18   7.06e-20   5.18e-18  -2.83e-18
46 -3.04e-16     2.67e-17      3.00e-17   2.60e-16   2.55e-16   1.78e-16
47 -2.48e-16     1.20e-18     -7.52e-18   2.28e-16   3.15e-16   2.16e-16
48 -1.32e-17    -1.39e-17     -1.02e-17   1.27e-17   2.07e-17   2.88e-17
    dfb.VARI dfb.ZnCs dfb.BLOQUEII. dfb.BLOQUEIII. dfb.DOSIS1. dfb.DOSIS2.
1   1.35e-01  0.15068     -5.84e-02      -5.84e-02   -9.53e-02   -9.53e-02
2  -4.48e-01 -0.35063     -1.94e-01       7.16e-16    3.17e-01    3.17e-01
3   3.10e-01  0.24230     -1.91e-16       1.34e-01   -2.19e-01   -2.19e-01
4  -6.10e-01  0.13648     -2.64e-01      -2.64e-01    4.32e-01    4.32e-01
5  -1.92e-02 -0.00215      8.33e-03       1.31e-17    1.36e-02    1.36e-02
6   6.31e-01  0.07055     -3.34e-16      -2.73e-01   -4.46e-01   -4.46e-01
7  -3.31e-16  0.13648     -2.64e-01      -2.64e-01    4.32e-01    1.08e-16
8   2.27e-16  0.05009     -1.94e-01      -1.65e-17   -3.17e-01   -1.73e-16
9   7.55e-17  0.01723     -3.63e-17      -6.67e-02   -1.09e-01   -9.02e-18
10 -2.01e-16 -0.07361      1.43e-01       1.43e-01    2.33e-01    5.85e-17
11 -8.30e-17 -0.05457      2.11e-01       6.22e-17   -3.45e-01    9.50e-17
12 -2.82e-17  0.01723     -1.36e-17      -6.67e-02    1.09e-01   -3.14e-17
13 -2.18e-16 -0.07361      1.43e-01       1.43e-01    1.81e-16   -2.33e-01
14  6.37e-16  0.10687     -4.14e-01      -3.71e-16   -5.63e-16   -6.76e-01
15 -6.18e-16 -0.15349      6.87e-16       5.94e-01    5.93e-16    9.71e-01
16  2.44e-16  0.06485     -1.26e-01      -1.26e-01   -2.28e-16   -2.05e-01
17  9.32e-16  0.08709     -3.37e-01      -2.49e-16   -6.73e-16    5.51e-01
18 -1.01e-16 -0.05233      1.38e-17       2.03e-01    1.84e-17   -3.31e-01
19 -6.79e-16 -0.14576      2.82e-01       2.82e-01    6.19e-16    7.06e-16
20 -1.05e-15 -0.13338      5.17e-01       4.70e-16    6.40e-16    7.95e-16
21  7.15e-17  0.05233     -8.27e-17      -2.03e-01   -4.32e-17   -1.95e-17
22 -2.10e-16 -0.07361      1.43e-01       1.43e-01    1.70e-16    1.23e-16
23 -4.92e-16 -0.11199      4.34e-01       3.15e-16    4.93e-16    4.17e-16
24  8.87e-17  0.07055     -3.72e-17      -2.73e-01   -1.49e-16    0.00e+00
25 -1.76e-16 -0.47859      1.85e-01       1.85e-01    3.12e-16   -5.19e-17
26  9.00e-17  0.30393      1.68e-01      -6.71e-17   -1.55e-16    1.37e-16
27  1.17e-17  0.03010      1.13e-18       1.67e-02   -2.43e-17    1.21e-18
28 -1.71e-16 -0.13188      2.55e-01       2.55e-01    1.69e-16    3.07e-16
29 -7.80e-19 -0.07992      3.10e-01       1.36e-16    1.28e-16   -1.85e-16
30 -5.35e-17  0.01291      1.02e-17      -5.00e-02    3.63e-17    6.93e-17
31  6.99e-17  0.11366     -2.20e-01      -2.20e-01    7.18e-17   -4.99e-17
32 -2.44e-17  0.00860     -3.33e-02      -6.54e-18    1.90e-17    1.41e-17
33  3.08e-16  0.04786     -3.78e-17      -1.85e-01   -4.28e-16   -2.13e-16
34 -2.01e-16 -0.06049      1.17e-01       1.17e-01    2.53e-16    1.14e-16
35  1.48e-16  0.04342     -1.68e-01      -7.70e-18   -7.44e-17   -1.57e-16
36 -1.81e-16 -0.07522      0.00e+00       2.91e-01    2.85e-16    1.18e-16
37  4.21e-17  0.07801     -1.51e-01      -1.51e-01   -4.42e-17   -5.39e-17
38 -6.81e-17  0.07992     -3.10e-01       7.90e-17   -1.13e-16    8.90e-17
39  2.22e-17 -0.03900      3.08e-17       1.51e-01   -1.62e-17   -1.06e-16
40  3.00e-18  0.00860     -1.67e-02      -1.67e-02   -8.14e-18    1.55e-18
41 -8.82e-17 -0.04342      1.68e-01      -3.19e-17    9.83e-17   -7.05e-18
42  1.34e-16  0.04786     -5.04e-17      -1.85e-01   -5.67e-17   -1.60e-16
43 -1.70e-16 -0.09572      1.85e-01       1.85e-01    1.31e-16    1.56e-16
44 -1.98e-17 -0.04342      1.68e-01      -4.73e-17    9.80e-17   -1.11e-17
45 -3.51e-18 -0.00430      0.00e+00       1.67e-02    2.24e-18   -4.98e-18
46  4.36e-16  0.18876     -3.66e-01      -3.66e-01   -2.78e-16   -3.00e-16
47  4.10e-16  0.07992     -3.10e-01       1.42e-17   -3.73e-16   -4.40e-16
48  1.07e-17  0.01291     -3.40e-18      -5.00e-02   -5.40e-18   -1.31e-17
   dfb.DOSIS3. dfb.ZnC.DOSIS1 dfb.ZnC.DOSIS2 dfb.ZnC.DOSIS3  dfb.ZC.V
1    -9.53e-02      -9.53e-02      -9.53e-02      -9.53e-02 -9.53e-02
2     3.17e-01       3.17e-01       3.17e-01       3.17e-01  3.17e-01
3    -2.19e-01      -2.19e-01      -2.19e-01      -2.19e-01 -2.19e-01
4     4.32e-01      -5.12e-16      -2.95e-16      -9.05e-17  4.32e-01
5     1.36e-02       1.17e-17      -1.55e-17       8.47e-19  1.36e-02
6    -4.46e-01      -4.37e-16      -2.91e-16      -5.74e-16 -4.46e-01
7     1.19e-16       4.32e-01       2.50e-16       9.78e-17  3.73e-16
8    -7.36e-17      -3.17e-01       1.67e-16       3.02e-16  4.57e-17
9    -5.68e-17      -1.09e-01      -1.19e-17      -8.02e-17 -8.90e-17
10    5.87e-17       1.68e-16       7.41e-17       4.09e-17  5.60e-17
11    1.04e-16       2.78e-16       1.28e-16       1.30e-16  1.33e-16
12    2.47e-17       7.92e-17      -5.99e-17       6.17e-17  4.71e-17
13    1.07e-16       1.94e-16      -2.33e-01       1.00e-16  1.76e-16
14   -5.27e-16      -1.13e-16      -6.76e-01       3.25e-17 -3.87e-16
15    6.24e-16       4.85e-16       9.71e-01       6.55e-16  8.43e-16
16   -2.85e-16      -2.20e-16      -1.17e-16      -2.34e-16 -2.57e-16
17   -5.32e-16      -6.95e-16      -1.13e-15      -6.35e-16 -8.65e-16
18    4.69e-18      -4.08e-17      -1.19e-16      -3.75e-18 -2.46e-18
19   -4.61e-01       5.51e-16       7.33e-16      -4.61e-01  7.11e-16
20    8.44e-01       6.97e-16       5.46e-16       8.44e-01  7.94e-16
21   -3.31e-01      -2.91e-17       7.79e-17      -3.31e-01 -1.36e-16
22    2.33e-01       1.93e-16       1.57e-16       1.90e-16  1.39e-16
23   -7.08e-01       4.47e-16       4.85e-16       3.85e-16  4.87e-16
24    4.46e-01       5.81e-17       1.85e-16       2.12e-16 -8.11e-17
25    6.26e-17       3.03e-01       3.03e-01       3.03e-01  3.03e-01
26   -3.81e-17      -2.75e-01      -2.75e-01      -2.75e-01 -2.75e-01
27   -9.32e-18      -2.72e-02      -2.72e-02      -2.72e-02 -2.72e-02
28    1.08e-16      -1.12e-16       2.18e-16       2.36e-18 -4.17e-01
29    7.16e-18       2.31e-16      -1.49e-16       1.69e-16  5.05e-01
30    4.88e-17       4.88e-17       1.04e-16       5.60e-17 -8.17e-02
31   -5.40e-17       3.59e-01      -1.80e-17       2.04e-17 -1.73e-17
32    1.88e-17      -5.44e-02       1.36e-17       1.22e-17  3.14e-17
33   -1.99e-16      -3.03e-01      -1.90e-16      -2.44e-16 -2.91e-16
34    1.36e-16       1.99e-16       5.92e-17       9.21e-17  1.56e-16
35   -1.57e-16      -9.55e-18      -1.35e-16      -1.22e-16 -9.24e-17
36    1.83e-16       3.67e-16       2.73e-16       2.72e-16  3.20e-16
37    3.49e-18      -1.37e-17       2.47e-01       1.54e-17  2.21e-17
38   -5.01e-17       2.81e-17      -5.05e-01      -1.86e-17  8.97e-17
39    1.61e-17      -1.23e-16       2.47e-01      -2.66e-17 -3.90e-17
40   -3.31e-18      -4.37e-18       9.90e-18      -2.62e-18  3.50e-19
41    5.06e-17       9.27e-17      -9.56e-18       1.32e-17  1.14e-17
42   -3.52e-17      -4.23e-17      -1.59e-16      -6.86e-17 -1.52e-16
43    1.27e-16       1.55e-16       2.14e-16      -3.03e-01  1.25e-16
44    1.56e-17       3.94e-17      -6.47e-17       2.75e-01 -4.27e-18
45    3.39e-18      -6.85e-18      -1.60e-17       2.72e-02 -4.48e-18
46   -2.84e-16      -2.87e-16      -2.60e-16      -2.03e-16 -3.96e-16
47   -3.44e-16      -2.81e-16      -4.08e-16      -3.09e-16 -5.29e-16
48   -1.67e-17      -8.97e-18      -1.83e-17      -2.22e-17 -5.28e-18
   dfb.ZC.DOSIS1. dfb.ZC.DOSIS2. dfb.ZC.DOSIS3.   dffit  cov.r   cook.d   hat
1        6.74e-02       6.74e-02       6.74e-02 -0.2131 3.3849 2.35e-03 0.417
2       -2.24e-01      -2.24e-01      -2.24e-01  0.7084 2.1225 2.54e-02 0.417
3        1.55e-01       1.55e-01       1.55e-01 -0.4895 2.7715 1.23e-02 0.417
4       -3.05e-01      -3.05e-01      -3.05e-01 -0.9651 1.3814 4.61e-02 0.417
5       -9.62e-03      -9.62e-03      -9.62e-03 -0.0304 3.5445 4.79e-05 0.417
6        3.16e-01       3.16e-01       3.16e-01  0.9978 1.2965 4.91e-02 0.417
7       -3.05e-01      -2.09e-16      -1.40e-16 -0.9651 1.3814 4.61e-02 0.417
8        2.24e-01      -6.21e-17      -1.14e-16  0.7084 2.1225 2.54e-02 0.417
9        7.70e-02       3.13e-18       8.90e-17  0.2436 3.3364 3.07e-03 0.417
10      -1.65e-01       2.70e-17       5.88e-17  0.5205 2.6840 1.39e-02 0.417
11       2.44e-01      -9.39e-17      -1.41e-16 -0.7718 1.9308 3.00e-02 0.417
12      -7.70e-02       3.66e-17      -8.90e-17  0.2436 3.3364 3.07e-03 0.417
13      -1.19e-16       1.65e-01      -9.51e-17  0.5205 2.6840 1.39e-02 0.417
14       4.51e-16       4.78e-01       3.74e-16  1.5113 0.3782 1.06e-01 0.417
15      -8.00e-16      -6.86e-01      -7.47e-16 -2.1707 0.0448 1.96e-01 0.417
16       2.25e-16       1.45e-01       2.93e-16 -0.4586 2.8561 1.08e-02 0.417
17       6.49e-16      -3.89e-01       5.69e-16  1.2316 0.7805 7.29e-02 0.417
18       5.20e-17       2.34e-01       0.00e+00 -0.7400 2.0265 2.76e-02 0.417
19      -6.18e-16      -7.68e-16       3.26e-01  1.0307 1.2141 5.22e-02 0.417
20      -5.73e-16      -5.27e-16      -5.96e-01 -1.8863 0.1201 1.56e-01 0.417
21       8.71e-17       2.76e-17       2.34e-01  0.7400 2.0265 2.76e-02 0.417
22      -1.48e-16      -8.72e-17      -1.65e-01  0.5205 2.6840 1.39e-02 0.417
23      -4.53e-16      -4.42e-16       5.01e-01 -1.5838 0.3075 1.15e-01 0.417
24       1.45e-16      -3.72e-17      -3.16e-01  0.9978 1.2965 4.91e-02 0.417
25      -2.14e-01      -2.14e-01      -2.14e-01 -0.6768 2.2185 2.32e-02 0.417
26       1.94e-01       1.94e-01       1.94e-01  0.6140 2.4088 1.92e-02 0.417
27       1.92e-02       1.92e-02       1.92e-02  0.0608 3.5343 1.92e-04 0.417
28       2.95e-01       2.95e-01       2.95e-01 -0.9325 1.4686 4.31e-02 0.417
29      -3.57e-01      -3.57e-01      -3.57e-01  1.1303 0.9836 6.21e-02 0.417
30       5.77e-02       5.77e-02       5.77e-02 -0.1826 3.4274 1.73e-03 0.417
31      -2.54e-01       5.08e-17       4.32e-18  0.8037 1.8358 3.24e-02 0.417
32       3.85e-02      -2.42e-17      -2.75e-17 -0.1217 3.4938 7.67e-04 0.417
33       2.14e-01       1.86e-16       2.18e-16 -0.6768 2.2185 2.32e-02 0.417
34      -1.35e-01      -8.22e-17      -1.13e-16 -0.4277 2.9374 9.40e-03 0.417
35      -1.94e-01       1.22e-16       9.90e-17 -0.6140 2.4088 1.92e-02 0.417
36       3.36e-01      -2.04e-16      -2.06e-16  1.0637 1.1344 5.54e-02 0.417
37      -2.90e-17      -1.74e-01      -6.52e-17  0.5516 2.5942 1.55e-02 0.417
38       1.59e-16       3.57e-01       6.08e-17 -1.1303 0.9836 6.21e-02 0.417
39       9.68e-18      -1.74e-01      -2.37e-17  0.5516 2.5942 1.55e-02 0.417
40       6.41e-18       1.92e-02       1.96e-18  0.0608 3.5343 1.92e-04 0.417
41      -3.23e-17       1.94e-01       1.98e-17  0.6140 2.4088 1.92e-02 0.417
42       5.94e-17      -2.14e-01       2.91e-17 -0.6768 2.2185 2.32e-02 0.417
43      -9.45e-17      -1.76e-16       2.14e-01 -0.6768 2.2185 2.32e-02 0.417
44      -7.10e-17       4.57e-17      -1.94e-01  0.6140 2.4088 1.92e-02 0.417
45       4.22e-18       1.59e-17      -1.92e-02  0.0608 3.5343 1.92e-04 0.417
46       2.23e-16       2.49e-16       4.22e-01  1.3347 0.6061 8.46e-02 0.417
47       4.47e-16       5.68e-16      -3.57e-01 -1.1303 0.9836 6.21e-02 0.417
48       1.33e-18       1.36e-17      -5.77e-02 -0.1826 3.4274 1.73e-03 0.417
   inf
1    *
2     
3     
4     
5    *
6     
7     
8     
9    *
10    
11    
12   *
13    
14    
15   *
16    
17    
18    
19    
20   *
21    
22    
23    
24    
25    
26    
27   *
28    
29    
30   *
31    
32   *
33    
34    
35    
36    
37    
38    
39    
40   *
41    
42    
43    
44    
45   *
46    
47    
48   *
influenceIndexPlot(modelo.dbca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dbca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1     -0.43657718      2.870777  0.2524
   2     -0.07139262      2.089374  0.8112
   3     -0.01979866      1.929698  0.5644
   4     -0.08805928      2.039234  0.3020
   5      0.41666667      1.018568  0.0244
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dbca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dbca
DW = 2.8708, p-value = 0.2701
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.dbca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dbca)
W = 0.96824, p-value = 0.2162
ad.test(rstudent(modelo.dbca))

    Anderson-Darling normality test

data:  rstudent(modelo.dbca)
A = 0.5146, p-value = 0.183
lillie.test(rstudent(modelo.dbca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dbca)
D = 0.14251, p-value = 0.01599
ks.test(rstudent(modelo.dbca), "pnorm",
        alternative = "two.sided")

    Asymptotic one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dbca)
D = 0.14768, p-value = 0.246
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dbca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dbca)
W = 0.086058, p-value = 0.1685
pearson.test(rstudent(modelo.dbca))

    Pearson chi-square normality test

data:  rstudent(modelo.dbca)
P = 11.167, p-value = 0.1315
sf.test(rstudent(modelo.dbca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dbca)
W = 0.97236, p-value = 0.2651

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dbca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 0.10062, Df = 1, p = 0.75109
bptest(modelo.dbca)

    studentized Breusch-Pagan test

data:  modelo.dbca
BP = 24.394, df = 19, p-value = 0.1815
bptest(modelo.dbca, studentize = F)

    Breusch-Pagan test

data:  modelo.dbca
BP = 15.27, df = 19, p-value = 0.7053
olsrr::ols_test_breusch_pagan(modelo.dbca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

                      Data                       
 ------------------------------------------------
 Response : Diametro_tallo_90dds 
 Variables: fitted values of Diametro_tallo_90dds 

        Test Summary         
 ----------------------------
 DF            =    1 
 Chi2          =    0.10062 
 Prob > Chi2   =    0.7510868 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dbca %>% gvlma()

Call:
lm(formula = Diametro_tallo_90dds ~ BLOQUE + BLOQUE %in% Zona + 
    DOSIS * VARIEDAD * Zona, data = data)

Coefficients:
                  (Intercept)                       BLOQUEII  
                    7.646e-01                     -1.250e-02  
                    BLOQUEIII                         DOSIS1  
                    1.875e-02                     -1.381e-15  
                       DOSIS2                         DOSIS3  
                   -5.000e-02                      6.667e-02  
                    VARIEDAD2                   ZonaCastilla  
                   -5.000e-02                     -6.875e-02  
        BLOQUEII:ZonaCastilla         BLOQUEIII:ZonaCastilla  
                    7.500e-02                     -1.875e-02  
             DOSIS1:VARIEDAD2               DOSIS2:VARIEDAD2  
                   -5.000e-02                      6.667e-02  
             DOSIS3:VARIEDAD2            ZonaCastilla:DOSIS1  
                   -1.667e-01                      5.000e-02  
          ZonaCastilla:DOSIS2            ZonaCastilla:DOSIS3  
                    1.167e-01                     -6.667e-02  
       ZonaCastilla:VARIEDAD2  ZonaCastilla:DOSIS1:VARIEDAD2  
                    1.667e-02                      6.667e-02  
ZonaCastilla:DOSIS2:VARIEDAD2  ZonaCastilla:DOSIS3:VARIEDAD2  
                   -1.000e-01                      2.667e-01  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                     Value  p-value                   Decision
Global Stat        10.2068 0.037084 Assumptions NOT satisfied!
Skewness            0.7767 0.378153    Assumptions acceptable.
Kurtosis            1.1192 0.290098    Assumptions acceptable.
Link Function       8.1303 0.004353 Assumptions NOT satisfied!
Heteroscedasticity  0.1807 0.670787    Assumptions acceptable.

Análisis de varianza

\[Y_{ijkl} = \mu + \delta_l + \tau_{i} + \text{Error}(\tau\text{Bloque})_{i(l)} + \beta_{j} + \gamma_{k} + \epsilon_{ijkl}\] \[\hat{Y}_{ijkl} = \mu + \delta_l + \tau_{i} + \text{Error}(\tau\text{Bloque})_{i(l)} + \beta_{j} + \gamma_{k}\]

Dónde:

\(Y_{ijkl}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijkl}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor Zona.

\(\text{Error}(\tau\text{Bloque})_{i(l)}\) = Efecto del i-ésimo nivel de Zona en el l-ésimo nivel de Bloque.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor tratamiento (Variedad).

\(\gamma_{k}\) = Efecto del k-ésimo nivel del factor tratamiento (Dosis).

\(\delta_{l}\) = Efecto del l-ésimo nivel del factor Bloque.

\(\epsilon_{ijkl}\) = Residuo observado del modelo.

Pruebas de hipótesis

Para el factor A (Zona):

\(H_0: \tau_{A1} = \tau_{A2} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (Variedad):

\(H_0: \beta_{B1} = \beta_{B2} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Para el factor C (Dosis):

\(H_0: \gamma_{C1} = \gamma_{C2} = 0\)

\(H_1: \text{En al menos un nivel del factor C el } \beta \text{ es diferente a los demás.}\)

\(H_1: \gamma_k \neq 0\text{; en al menos un nivel del factor C.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dbca, test = "F")
Analysis of Variance Table

Response: Diametro_tallo_90dds
                    Df   Sum Sq   Mean Sq F value  Pr(>F)  
BLOQUE               2 0.005104 0.0025521  0.4604 0.63572  
DOSIS                3 0.002500 0.0008333  0.1503 0.92860  
VARIEDAD             1 0.030000 0.0300000  5.4121 0.02746 *
Zona                 1 0.001875 0.0018750  0.3383 0.56549  
BLOQUE:Zona          2 0.019688 0.0098438  1.7758 0.18789  
DOSIS:VARIEDAD       3 0.004167 0.0013889  0.2506 0.86025  
Zona:DOSIS           3 0.012292 0.0040972  0.7391 0.53762  
Zona:VARIEDAD        1 0.016875 0.0168750  3.0443 0.09199 .
Zona:DOSIS:VARIEDAD  3 0.053958 0.0179861  3.2447 0.03678 *
Residuals           28 0.155208 0.0055432                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
GAD::estimates(modelo.dbca)
$tm
                    BLOQUE Zona DOSIS VARIEDAD   n
BLOQUE                   1    2     4        2 2.4
DOSIS                    3    2     0        2 2.4
VARIEDAD                 3    2     4        0 2.4
Zona                     3    0     4        2 2.4
BLOQUE:Zona              1    0     4        2 2.4
DOSIS:VARIEDAD           3    2     0        0 2.4
Zona:DOSIS               3    0     0        2 2.4
Zona:VARIEDAD            3    0     4        0 2.4
Zona:DOSIS:VARIEDAD      3    0     0        0 2.4
Res                      1    1     1        1 1.0

$mse
                    Mean square estimates      
BLOQUE              "Res + BLOQUE"             
DOSIS               "Res + DOSIS"              
VARIEDAD            "Res + VARIEDAD"           
Zona                "Res + BLOQUE:Zona + Zona" 
BLOQUE:Zona         "Res + BLOQUE:Zona"        
DOSIS:VARIEDAD      "Res + DOSIS:VARIEDAD"     
Zona:DOSIS          "Res + Zona:DOSIS"         
Zona:VARIEDAD       "Res + Zona:VARIEDAD"      
Zona:DOSIS:VARIEDAD "Res + Zona:DOSIS:VARIEDAD"
Residual            "Res"                      

$f.versus
                    F-ratio versus
BLOQUE              "Residual"    
DOSIS               "Residual"    
VARIEDAD            "Residual"    
Zona                "BLOQUE:Zona" 
BLOQUE:Zona         "Residual"    
DOSIS:VARIEDAD      "Residual"    
Zona:DOSIS          "Residual"    
Zona:VARIEDAD       "Residual"    
Zona:DOSIS:VARIEDAD "Residual"    
GAD::gad(modelo.dbca)
Analysis of Variance Table

Response: Diametro_tallo_90dds
                    Df   Sum Sq   Mean Sq F value  Pr(>F)  
BLOQUE               2 0.005104 0.0025521  0.4604 0.63572  
DOSIS                3 0.002500 0.0008333  0.1503 0.92860  
VARIEDAD             1 0.030000 0.0300000  5.4121 0.02746 *
Zona                 1 0.001875 0.0018750  0.1905 0.70512  
BLOQUE:Zona          2 0.019688 0.0098438  1.7758 0.18789  
DOSIS:VARIEDAD       3 0.004167 0.0013889  0.2506 0.86025  
Zona:DOSIS           3 0.012292 0.0040972  0.7391 0.53762  
Zona:VARIEDAD        1 0.016875 0.0168750  3.0443 0.09199 .
Zona:DOSIS:VARIEDAD  3 0.053958 0.0179861  3.2447 0.03678 *
Residual            28 0.155208 0.0055432                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(Zona/Bloque)” en el caso de efectos aleatorios o “Error(Zona:Bloque)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos.

aov(Diametro_tallo_90dds ~ BLOQUE + Zona * VARIEDAD * DOSIS + Error(BLOQUE %in% Zona), data = data) -> aov.dbca
summary(aov.dbca)

Error: BLOQUE:Zona
          Df   Sum Sq  Mean Sq F value Pr(>F)
BLOQUE     2 0.005104 0.002552   0.259  0.794
Zona       1 0.001875 0.001875   0.190  0.705
Residuals  2 0.019688 0.009844               

Error: Within
                    Df  Sum Sq  Mean Sq F value Pr(>F)  
VARIEDAD             1 0.03000 0.030000   5.412 0.0275 *
DOSIS                3 0.00250 0.000833   0.150 0.9286  
Zona:VARIEDAD        1 0.01688 0.016875   3.044 0.0920 .
Zona:DOSIS           3 0.01229 0.004097   0.739 0.5376  
VARIEDAD:DOSIS       3 0.00417 0.001389   0.251 0.8602  
Zona:VARIEDAD:DOSIS  3 0.05396 0.017986   3.245 0.0368 *
Residuals           28 0.15521 0.005543                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
broom::tidy(aov.dbca)
# A tibble: 10 × 7
   stratum     term                   df   sumsq   meansq statistic p.value
   <chr>       <chr>               <dbl>   <dbl>    <dbl>     <dbl>   <dbl>
 1 BLOQUE:Zona BLOQUE                  2 0.00510 0.00255      0.259  0.794 
 2 BLOQUE:Zona Zona                    1 0.00187 0.00187      0.190  0.705 
 3 BLOQUE:Zona Residuals               2 0.0197  0.00984     NA     NA     
 4 Within      VARIEDAD                1 0.0300  0.0300       5.41   0.0275
 5 Within      DOSIS                   3 0.00250 0.000833     0.150  0.929 
 6 Within      Zona:VARIEDAD           1 0.0169  0.0169       3.04   0.0920
 7 Within      Zona:DOSIS              3 0.0123  0.00410      0.739  0.538 
 8 Within      VARIEDAD:DOSIS          3 0.00417 0.00139      0.251  0.860 
 9 Within      Zona:VARIEDAD:DOSIS     3 0.0540  0.0180       3.24   0.0368
10 Within      Residuals              28 0.155   0.00554     NA     NA     
broom::tidy(gad(modelo.dbca))
# A tibble: 10 × 6
   term                   df   sumsq   meansq statistic p.value
   <chr>               <int>   <dbl>    <dbl>     <dbl>   <dbl>
 1 BLOQUE                  2 0.00510 0.00255      0.460  0.636 
 2 DOSIS                   3 0.00250 0.000833     0.150  0.929 
 3 VARIEDAD                1 0.0300  0.0300       5.41   0.0275
 4 Zona                    1 0.00187 0.00187      0.190  0.705 
 5 BLOQUE:Zona             2 0.0197  0.00984      1.78   0.188 
 6 DOSIS:VARIEDAD          3 0.00417 0.00139      0.251  0.860 
 7 Zona:DOSIS              3 0.0123  0.00410      0.739  0.538 
 8 Zona:VARIEDAD           1 0.0169  0.0169       3.04   0.0920
 9 Zona:DOSIS:VARIEDAD     3 0.0540  0.0180       3.24   0.0368
10 Residual               28 0.155   0.00554     NA     NA     

Valor de la tabla de F para el factor Zona con una significancia de 0.05.

qf(0.95, 1, 2)
[1] 18.51282

Valor de la tabla de F para el factor Variedad con una significancia de 0.05.

qf(0.95, 1, 28)
[1] 4.195972

Valor de la tabla de F para el factor Dosis con una significancia de 0.05.

qf(0.95, 3, 28)
[1] 2.946685

Conclusión.

Con respecto al Factor Zona: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor Zona tienen un efecto sobre el diámetro de tallo estadísticamente similar a 0.

Con respecto al Factor Variedad: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor Variedad tienen un efecto sobre el diámetro de tallo estadísticamente similar a 0.

Con respecto al Factor Dosis: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor Dosis tienen un efecto sobre el diámetro de tallo estadísticamente similar a 0.

Con respecto a la interacción entre Zona/Variedad/Dosis: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, existe al menos un nivel de interacción estadísticamente antagonista y sinergista con respecto al diámetro de tallo.

agricolae::cv.model(modelo.dbca)
[1] 10.1526

Comparaciones de medias para los efectos principales del Factor Zona

get_df_ea <- function(object) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  df_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(":", stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(df)
  return(df_rep_A_residuals)
}
get_df_ea(aov.dbca)
[1] 2
get_mse_ea <- function(object) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  meansq_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(":", stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(meansq)
  return(meansq_rep_A_residuals)
}
get_mse_ea(aov.dbca)
[1] 0.00984375
data %>% with(LSD.test(
  Diametro_tallo_90dds, # Cambiar según nombre de variable respuesta
  Zona, # Cambiar según nombre de variable independiente
  DFerror = get_df_ea(aov.dbca), 
  MSerror = get_mse_ea(aov.dbca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: Diametro_tallo_90dds ~ Zona

LSD t Test for Diametro_tallo_90dds 

Mean Square Error:  0.00984375 

Zona,  means and individual ( 95 %) CI

         Diametro_tallo_90dds        std  r       LCL      UCL Min  Max
Camana              0.7270833 0.09205288 24 0.6399447 0.814222 0.5 0.90
Castilla            0.7395833 0.06753287 24 0.6524447 0.826722 0.6 0.85

Alpha: 0.05 ; DF Error: 2
Critical Value of t: 4.302653 

least Significant Difference: 0.1232327 

Treatments with the same letter are not significantly different.

         Diametro_tallo_90dds groups
Castilla            0.7395833      a
Camana              0.7270833      a

Comparaciones de medias para los efectos principales del Factor Variedad

data %>% with(LSD.test(
  Diametro_tallo_90dds, # Cambiar según nombre de variable respuesta
  VARIEDAD, # Cambiar según nombre de variable independiente
  DFerror = df.residual(modelo.dbca), 
  MSerror = dvmisc::get_mse(modelo.dbca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: Diametro_tallo_90dds ~ VARIEDAD

LSD t Test for Diametro_tallo_90dds 

Mean Square Error:  0.005543155 

VARIEDAD,  means and individual ( 95 %) CI

  Diametro_tallo_90dds        std  r       LCL       UCL Min  Max
1            0.7583333 0.07322786 24 0.7272026 0.7894641 0.6 0.90
2            0.7083333 0.08030738 24 0.6772026 0.7394641 0.5 0.85

Alpha: 0.05 ; DF Error: 28
Critical Value of t: 2.048407 

least Significant Difference: 0.04402549 

Treatments with the same letter are not significantly different.

  Diametro_tallo_90dds groups
1            0.7583333      a
2            0.7083333      b

Comparaciones de medias para las interacciones

Para cada Zona, se debe aplicar lo siguiente:

Para los niveles del factor B dentro del nivel C1:

  • B1 vs B2:

\(H_0: \mu_{B1} - \mu_{B2} = 0\)

\(H_1: \mu_{B1} - \mu_{B2} \neq 0\)

  • B3 vs B4:

\(H_0: \mu_{B3} - \mu_{B4} = 0\)

\(H_1: \mu_{B4} - \mu_{B4} \neq 0\)

Para los niveles del factor C dentro del nivel B1:

  • C1 vs C2:

\(H_0: \mu_{C1} - \mu_{C2} = 0\)

\(H_1: \mu_{C1} - \mu_{C2} \neq 0\)

NOTA: Repetir este proceso para cada nivel de B y cada nivel de C.

Análisis de varianza para interacción de tres factores con el paquete emmeans

Comparación de la interacción de los niveles de B y los niveles de C dentro de cada nivel de A

emmeans::joint_tests(modelo.dbca, by = "Zona")
Zona = Camana:
 model term     df1 df2 F.ratio p.value
 BLOQUE           2  28   0.357  0.7029
 DOSIS            3  28   0.119  0.9482
 VARIEDAD         1  28   8.287  0.0076
 DOSIS:VARIEDAD   3  28   2.625  0.0701

Zona = Castilla:
 model term     df1 df2 F.ratio p.value
 BLOQUE           2  28   1.879  0.1715
 DOSIS            3  28   0.770  0.5203
 VARIEDAD         1  28   0.169  0.6840
 DOSIS:VARIEDAD   3  28   0.871  0.4679
emmeans::joint_tests(modelo.dbca, by = c("Zona","VARIEDAD"))
Zona = Camana, VARIEDAD = 1:
 model term df1 df2 F.ratio p.value
 BLOQUE       2  28   0.357  0.7029
 DOSIS        3  28   1.240  0.3138

Zona = Castilla, VARIEDAD = 1:
 model term df1 df2 F.ratio p.value
 BLOQUE       2  28   1.879  0.1715
 DOSIS        3  28   0.639  0.5963

Zona = Camana, VARIEDAD = 2:
 model term df1 df2 F.ratio p.value
 BLOQUE       2  28   0.357  0.7029
 DOSIS        3  28   1.503  0.2353

Zona = Castilla, VARIEDAD = 2:
 model term df1 df2 F.ratio p.value
 BLOQUE       2  28   1.879  0.1715
 DOSIS        3  28   1.002  0.4064
emmeans::joint_tests(modelo.dbca, by = c("Zona","DOSIS"))
Zona = Camana, DOSIS = 0:
 model term df1 df2 F.ratio p.value
 BLOQUE       2  28   0.357  0.7029
 VARIEDAD     1  28   0.677  0.4177

Zona = Castilla, DOSIS = 0:
 model term df1 df2 F.ratio p.value
 BLOQUE       2  28   1.879  0.1715
 VARIEDAD     1  28   0.301  0.5878

Zona = Camana, DOSIS = 1:
 model term df1 df2 F.ratio p.value
 BLOQUE       2  28   0.357  0.7029
 VARIEDAD     1  28   2.706  0.1112

Zona = Castilla, DOSIS = 1:
 model term df1 df2 F.ratio p.value
 BLOQUE       2  28   1.879  0.1715
 VARIEDAD     1  28   0.075  0.7860

Zona = Camana, DOSIS = 2:
 model term df1 df2 F.ratio p.value
 BLOQUE       2  28   0.357  0.7029
 VARIEDAD     1  28   0.075  0.7860

Zona = Castilla, DOSIS = 2:
 model term df1 df2 F.ratio p.value
 BLOQUE       2  28   1.879  0.1715
 VARIEDAD     1  28   1.203  0.2821

Zona = Camana, DOSIS = 3:
 model term df1 df2 F.ratio p.value
 BLOQUE       2  28   0.357  0.7029
 VARIEDAD     1  28  12.703  0.0013

Zona = Castilla, DOSIS = 3:
 model term df1 df2 F.ratio p.value
 BLOQUE       2  28   1.879  0.1715
 VARIEDAD     1  28   1.203  0.2821
emm <- emmeans::emmeans(modelo.dbca, ~ VARIEDAD | DOSIS | Zona)
multcomp::cld(emm, Letters=LETTERS, adjust = "none")
DOSIS = 0, Zona = Camana:
 VARIEDAD emmean    SE df lower.CL upper.CL .group
 2         0.717 0.043 28    0.629    0.805  A    
 1         0.767 0.043 28    0.679    0.855  A    

DOSIS = 1, Zona = Camana:
 VARIEDAD emmean    SE df lower.CL upper.CL .group
 2         0.667 0.043 28    0.579    0.755  A    
 1         0.767 0.043 28    0.679    0.855  A    

DOSIS = 2, Zona = Camana:
 VARIEDAD emmean    SE df lower.CL upper.CL .group
 1         0.717 0.043 28    0.629    0.805  A    
 2         0.733 0.043 28    0.645    0.821  A    

DOSIS = 3, Zona = Camana:
 VARIEDAD emmean    SE df lower.CL upper.CL .group
 2         0.617 0.043 28    0.529    0.705  A    
 1         0.833 0.043 28    0.745    0.921   B   

DOSIS = 0, Zona = Castilla:
 VARIEDAD emmean    SE df lower.CL upper.CL .group
 2         0.683 0.043 28    0.595    0.771  A    
 1         0.717 0.043 28    0.629    0.805  A    

DOSIS = 1, Zona = Castilla:
 VARIEDAD emmean    SE df lower.CL upper.CL .group
 2         0.750 0.043 28    0.662    0.838  A    
 1         0.767 0.043 28    0.679    0.855  A    

DOSIS = 2, Zona = Castilla:
 VARIEDAD emmean    SE df lower.CL upper.CL .group
 2         0.717 0.043 28    0.629    0.805  A    
 1         0.783 0.043 28    0.695    0.871  A    

DOSIS = 3, Zona = Castilla:
 VARIEDAD emmean    SE df lower.CL upper.CL .group
 1         0.717 0.043 28    0.629    0.805  A    
 2         0.783 0.043 28    0.695    0.871  A    

Results are averaged over the levels of: BLOQUE 
Confidence level used: 0.95 
significance level used: alpha = 0.05 
NOTE: If two or more means share the same grouping symbol,
      then we cannot show them to be different.
      But we also did not show them to be the same. 
emm <- emmeans::emmeans(modelo.dbca, ~ DOSIS | VARIEDAD | Zona)
multcomp::cld(emm, Letters=LETTERS, adjust = "none")
VARIEDAD = 1, Zona = Camana:
 DOSIS emmean    SE df lower.CL upper.CL .group
 2      0.717 0.043 28    0.629    0.805  A    
 1      0.767 0.043 28    0.679    0.855  A    
 0      0.767 0.043 28    0.679    0.855  A    
 3      0.833 0.043 28    0.745    0.921  A    

VARIEDAD = 2, Zona = Camana:
 DOSIS emmean    SE df lower.CL upper.CL .group
 3      0.617 0.043 28    0.529    0.705  A    
 1      0.667 0.043 28    0.579    0.755  A    
 0      0.717 0.043 28    0.629    0.805  A    
 2      0.733 0.043 28    0.645    0.821  A    

VARIEDAD = 1, Zona = Castilla:
 DOSIS emmean    SE df lower.CL upper.CL .group
 0      0.717 0.043 28    0.629    0.805  A    
 3      0.717 0.043 28    0.629    0.805  A    
 1      0.767 0.043 28    0.679    0.855  A    
 2      0.783 0.043 28    0.695    0.871  A    

VARIEDAD = 2, Zona = Castilla:
 DOSIS emmean    SE df lower.CL upper.CL .group
 0      0.683 0.043 28    0.595    0.771  A    
 2      0.717 0.043 28    0.629    0.805  A    
 1      0.750 0.043 28    0.662    0.838  A    
 3      0.783 0.043 28    0.695    0.871  A    

Results are averaged over the levels of: BLOQUE 
Confidence level used: 0.95 
significance level used: alpha = 0.05 
NOTE: If two or more means share the same grouping symbol,
      then we cannot show them to be different.
      But we also did not show them to be the same. 

Plot de interacciones

phia::interactionMeans(model = modelo.dbca,
                       factors = c("Zona","VARIEDAD","DOSIS")) %>%
  plot()

Comparaciones de medias de cada Zona

filter_by_2factor_level <- function(data, factor_name1, factor_name2) {
  levels1 <- levels(data[[deparse(substitute(factor_name1))]])
  filters1 <- purrr::map(levels1, ~ filter(data, {{factor_name1}} == .x))
  names(filters1) <- levels1
  
  levels2 <- levels(data[[deparse(substitute(factor_name2))]])
  filters2 <- purrr::map(levels2, ~ filter(data, {{factor_name2}} == .x))
  names(filters2) <- levels2
  
  result <- list()
  result[[deparse(substitute(factor_name1))]] <- filters1
  result[[deparse(substitute(factor_name2))]] <- filters2
  return(result)
}
niveles_zona <- unique(data$Zona)

# Aplicar la función filter_by_2factor_level a cada nivel de Zona
datos_filtrados <- purrr::map(
  niveles_zona, 
  ~ filter_by_2factor_level(
      data = filter(data, Zona == .x),
      factor_name1 = VARIEDAD,
      factor_name2 = DOSIS))
names(datos_filtrados) <- niveles_zona
filter_by_3factor_level <- function(data, factor_name1, factor_name2, factor_name3) {
  levels1 <- levels(data[[deparse(substitute(factor_name2))]])
  levels2 <- levels(data[[deparse(substitute(factor_name3))]])
  levels3 <- levels(data[[deparse(substitute(factor_name1))]])
  
  result <- list()
  
  for (level3 in levels3) {
    filters1 <- purrr::map(levels1, ~ filter(data, {{ factor_name2 }} == .x & {{ factor_name1 }} == level3))
    names(filters1) <- levels1
    
    filters2 <- purrr::map(levels2, ~ filter(data, {{ factor_name3 }} == .x & {{ factor_name1 }} == level3))
    names(filters2) <- levels2
    
    result[[as.character(level3)]] <- list()
    result[[as.character(level3)]][[deparse(substitute(factor_name2))]] <- filters1
    result[[as.character(level3)]][[deparse(substitute(factor_name3))]] <- filters2
  }
  
  return(result)
}
datos_filtrados <- 
  filter_by_3factor_level(
    data = data,
    factor_name1 = Zona,
    factor_name2 = VARIEDAD,
    factor_name3 = DOSIS)
multcomp.test_3factors <- function(object, respuesta, factor_name1, factor_name2, test, aov){
  
  # Función auxiliar para aplicar la prueba de comparaciones múltiples a un data frame
  multcomp_df <- function(df, respuesta, factor_name, test, aov){
    if (test == "LSD") {
      comp <- LSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "HSD") {
      comp <- HSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "duncan") {
      comp <- duncan.test(df[[respuesta]],
                          df[[factor_name]],
                          DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                          group=TRUE,
                          main = NULL,
                          console=FALSE)[[6]]
    } else if (test == "SNK") {
      comp <- SNK.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[6]]
    } else {
      stop("Test no válido. Los tests disponibles son LSD, HSD, duncan, y SNK.")
    }
    
    return(comp %>%
             rename("y" = "df[[respuesta]]")
           )
  }
  
  # Obtener los nombres de la lista
  list_names <- names(object)
  
  # Aplicar la función multcomp.test_3factors a cada elemento de la lista
  result <- lapply(list_names, function(name) {
    df <- object[[name]]
    comp_filters1 <- lapply(df[[factor_name1]], function(df_factor1) {
      multcomp_df(df_factor1, respuesta, factor_name2, test, aov) %>%
        arrange(row.names(.)) %>%
        rownames_to_column(var = "x") %>%
        relocate(x)
    })
    
    comp_filters2 <- lapply(df[[factor_name2]], function(df_factor2) {
      multcomp_df(df_factor2, respuesta, factor_name1, test, aov) %>%
        arrange(row.names(.)) %>%
        rownames_to_column(var = "x") %>%
        relocate(x) %>%
        mutate(groups = toupper(groups))
    })
    
    row.names(comp_filters1) <- NULL
    row.names(comp_filters2) <- NULL
  
    # Retornar una lista con las comparaciones múltiples para cada data frame
    prev_result <- list()
    prev_result[[factor_name1]] <- comp_filters1
    prev_result[[factor_name2]] <- comp_filters2
    return(prev_result)
  })
  
  # Asignar los nombres de la lista
  names(result) <- list_names
  
  return(result)
}

Interacción de Variedad y Dosis dentro de la Zona 1

multcomp.test_3factors(
  object = datos_filtrados,
  respuesta = "Diametro_tallo_90dds",
  factor_name1 = "VARIEDAD",
  factor_name2 = "DOSIS",
  test = "LSD",
  aov = modelo.dbca) -> result.comp
result.comp
$Camana
$Camana$VARIEDAD
$Camana$VARIEDAD$`1`
  x         y groups
1 0 0.7666667      a
2 1 0.7666667      a
3 2 0.7166667      a
4 3 0.8333333      a

$Camana$VARIEDAD$`2`
  x         y groups
1 0 0.7166667      a
2 1 0.6666667      a
3 2 0.7333333      a
4 3 0.6166667      a


$Camana$DOSIS
$Camana$DOSIS$`0`
  x         y groups
1 1 0.7666667      A
2 2 0.7166667      A

$Camana$DOSIS$`1`
  x         y groups
1 1 0.7666667      A
2 2 0.6666667      A

$Camana$DOSIS$`2`
  x         y groups
1 1 0.7166667      A
2 2 0.7333333      A

$Camana$DOSIS$`3`
  x         y groups
1 1 0.8333333      A
2 2 0.6166667      B



$Castilla
$Castilla$VARIEDAD
$Castilla$VARIEDAD$`1`
  x         y groups
1 0 0.7166667      a
2 1 0.7666667      a
3 2 0.7833333      a
4 3 0.7166667      a

$Castilla$VARIEDAD$`2`
  x         y groups
1 0 0.6833333      a
2 1 0.7500000      a
3 2 0.7166667      a
4 3 0.7833333      a


$Castilla$DOSIS
$Castilla$DOSIS$`0`
  x         y groups
1 1 0.7166667      A
2 2 0.6833333      A

$Castilla$DOSIS$`1`
  x         y groups
1 1 0.7666667      A
2 2 0.7500000      A

$Castilla$DOSIS$`2`
  x         y groups
1 1 0.7833333      A
2 2 0.7166667      A

$Castilla$DOSIS$`3`
  x         y groups
1 1 0.7166667      A
2 2 0.7833333      A
# Convertir la lista a un data frame
df <- result.comp %>%
  reshape2::melt() %>% 
  ungroup() %>%
  dplyr::select(-variable) %>%
  relocate("Zona" = "L1",
           "Factor" = "L2",
           "Nivel" = "L3",
           x,
           "y" = "value",
           groups)
df
       Zona   Factor Nivel x         y groups
1    Camana VARIEDAD     1 0 0.7666667      a
2    Camana VARIEDAD     1 1 0.7666667      a
3    Camana VARIEDAD     1 2 0.7166667      a
4    Camana VARIEDAD     1 3 0.8333333      a
5    Camana VARIEDAD     2 0 0.7166667      a
6    Camana VARIEDAD     2 1 0.6666667      a
7    Camana VARIEDAD     2 2 0.7333333      a
8    Camana VARIEDAD     2 3 0.6166667      a
9    Camana    DOSIS     0 1 0.7666667      A
10   Camana    DOSIS     0 2 0.7166667      A
11   Camana    DOSIS     1 1 0.7666667      A
12   Camana    DOSIS     1 2 0.6666667      A
13   Camana    DOSIS     2 1 0.7166667      A
14   Camana    DOSIS     2 2 0.7333333      A
15   Camana    DOSIS     3 1 0.8333333      A
16   Camana    DOSIS     3 2 0.6166667      B
17 Castilla VARIEDAD     1 0 0.7166667      a
18 Castilla VARIEDAD     1 1 0.7666667      a
19 Castilla VARIEDAD     1 2 0.7833333      a
20 Castilla VARIEDAD     1 3 0.7166667      a
21 Castilla VARIEDAD     2 0 0.6833333      a
22 Castilla VARIEDAD     2 1 0.7500000      a
23 Castilla VARIEDAD     2 2 0.7166667      a
24 Castilla VARIEDAD     2 3 0.7833333      a
25 Castilla    DOSIS     0 1 0.7166667      A
26 Castilla    DOSIS     0 2 0.6833333      A
27 Castilla    DOSIS     1 1 0.7666667      A
28 Castilla    DOSIS     1 2 0.7500000      A
29 Castilla    DOSIS     2 1 0.7833333      A
30 Castilla    DOSIS     2 2 0.7166667      A
31 Castilla    DOSIS     3 1 0.7166667      A
32 Castilla    DOSIS     3 2 0.7833333      A
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # # Convertir level1 y level2 en nombres simbólicos
  # level1 <- as.name(level1)
  # level2 <- as.name(level2)
  # 
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1, level2)) %>%
    dplyr::mutate(groups = paste0(groups.y,groups.x)) %>%
    dplyr::select(!!level1,!!level2, y, groups) #%>%
    # rename(!!level1 := x,
    #        !!level2 := Nivel)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
zonas <- unique(df$Zona)

resultados <- zonas %>%
  map(~ create_report(filter(df, Zona == .x), "VARIEDAD", "DOSIS"))

names(resultados) <- zonas

resultados
$Camana
  VARIEDAD DOSIS         y groups
1        1     0 0.7666667     Aa
2        1     1 0.7666667     Aa
3        1     2 0.7166667     Aa
4        1     3 0.8333333     Aa
5        2     0 0.7166667     Aa
6        2     1 0.6666667     Aa
7        2     2 0.7333333     Aa
8        2     3 0.6166667     Ba

$Castilla
  VARIEDAD DOSIS         y groups
1        1     0 0.7166667     Aa
2        1     1 0.7666667     Aa
3        1     2 0.7833333     Aa
4        1     3 0.7166667     Aa
5        2     0 0.6833333     Aa
6        2     1 0.7500000     Aa
7        2     2 0.7166667     Aa
8        2     3 0.7833333     Aa
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1,level2)) %>%
    dplyr::mutate(y = paste0(round(y,2), " ", groups.y, groups.x)) %>%
    dplyr::select(!!level1,!!level2, y)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
apply_create_report <- function(df, level1, level2, ExpRep) {
  zonas <- unique(df[[ExpRep]])
  resultados <- purrr::map(zonas, ~ create_report(filter(df, .data[[ExpRep]] == .x), level1, level2))
  
  # Asignar los nombres de las zonas a los resultados
  names(resultados) <- zonas
  
  # Combinar los resultados en un data frame final
  df_final <- bind_rows(resultados, .id = ExpRep)
  
  return(df_final)
}
apply_create_report(df, "VARIEDAD", "DOSIS", "Zona") -> df2
df2
       Zona VARIEDAD DOSIS       y
1    Camana        1     0 0.77 Aa
2    Camana        1     1 0.77 Aa
3    Camana        1     2 0.72 Aa
4    Camana        1     3 0.83 Aa
5    Camana        2     0 0.72 Aa
6    Camana        2     1 0.67 Aa
7    Camana        2     2 0.73 Aa
8    Camana        2     3 0.62 Ba
9  Castilla        1     0 0.72 Aa
10 Castilla        1     1 0.77 Aa
11 Castilla        1     2 0.78 Aa
12 Castilla        1     3 0.72 Aa
13 Castilla        2     0 0.68 Aa
14 Castilla        2     1 0.75 Aa
15 Castilla        2     2 0.72 Aa
16 Castilla        2     3 0.78 Aa
df2 %>% 
 pivot_wider(names_from = DOSIS,
             values_from = c(y), 
             names_glue = "{DOSIS}") %>%
  gt()
Zona VARIEDAD 0 1 2 3
Camana 1 0.77 Aa 0.77 Aa 0.72 Aa 0.83 Aa
Camana 2 0.72 Aa 0.67 Aa 0.73 Aa 0.62 Ba
Castilla 1 0.72 Aa 0.77 Aa 0.78 Aa 0.72 Aa
Castilla 2 0.68 Aa 0.75 Aa 0.72 Aa 0.78 Aa

Experimentos repetidos en el tiempo y en el espacio


Importación de datos


archivos <- list.files(pattern = "datos exp. repetidos.xlsx", 
                       full.names = TRUE,
                       recursive = TRUE)

# Importación
data <- readxl::read_xlsx(archivos,
                           sheet = "espacio y tiempo")

# Preprocesamiento

data <- data %>%
  mutate_if(is.character, factor) %>%
  mutate(lugar = GAD::as.fixed(factor(lugar)),
         linaje = GAD::as.fixed(factor(linaje)),
         epoca = GAD::as.fixed(factor(epoca)),
         bloque = GAD::as.random(bloque))

data_D <- data %>%
  dplyr::filter(epoca %in% 1)

Análisis de DBCA de dos vías con análisis entre sitios


Definición del modelo


modelo.dbca <- lm(rdto ~ lugar * linaje + bloque %in% lugar + bloque, data = data_D)
summary(modelo.dbca)

Call:
lm(formula = rdto ~ lugar * linaje + bloque %in% lugar + bloque, 
    data = data_D)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.8333 -1.0625 -0.4167  1.7500  6.0000 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)           11.0833     1.9637   5.644 3.79e-06 ***
lugarPisco             1.9167     2.7771   0.690   0.4954    
linaje2               -0.1667     1.8514  -0.090   0.9289    
linaje3               -1.5000     1.8514  -0.810   0.4242    
linaje4               -3.6667     1.8514  -1.980   0.0569 .  
bloqueII               1.7500     2.2675   0.772   0.4463    
bloqueIII              0.7500     2.2675   0.331   0.7431    
bloqueIV               1.0000     2.2675   0.441   0.6624    
bloqueV                2.5000     2.2675   1.103   0.2790    
bloqueVI               2.5000     2.2675   1.103   0.2790    
lugarPisco:linaje2     2.3333     2.6183   0.891   0.3799    
lugarPisco:linaje3     2.5000     2.6183   0.955   0.3473    
lugarPisco:linaje4     3.5000     2.6183   1.337   0.1914    
lugarPisco:bloqueII    1.2500     3.2068   0.390   0.6994    
lugarPisco:bloqueIII  -1.0000     3.2068  -0.312   0.7573    
lugarPisco:bloqueIV    4.0000     3.2068   1.247   0.2219    
lugarPisco:bloqueV    -0.5000     3.2068  -0.156   0.8771    
lugarPisco:bloqueVI   -1.2500     3.2068  -0.390   0.6994    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.207 on 30 degrees of freedom
Multiple R-squared:  0.5675,    Adjusted R-squared:  0.3224 
F-statistic: 2.315 on 17 and 30 DF,  p-value: 0.02156

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dbca)
ggResidpanel::resid_panel(modelo.dbca)
influence.measures(modelo.dbca)
Influence measures of
     lm(formula = rdto ~ lugar * linaje + bloque %in% lugar + bloque,      data = data_D) :

      dfb.1_ dfb.lgrP  dfb.lnj2  dfb.lnj3  dfb.lnj4  dfb.blII  dfb.bIII
1   2.76e-01 -0.19514 -1.30e-01 -1.30e-01 -1.30e-01 -1.59e-01 -1.59e-01
2   1.67e-02 -0.01180 -2.36e-02 -2.36e-02 -2.36e-02  2.89e-02  1.60e-17
3  -8.36e-02  0.05911  1.18e-01  1.18e-01  1.18e-01  1.87e-16 -1.45e-01
4   9.20e-02 -0.06505 -1.30e-01 -1.30e-01 -1.30e-01 -2.49e-16 -2.52e-16
5  -2.63e-01  0.18617  3.72e-01  3.72e-01  3.72e-01  6.54e-16  6.10e-16
6   1.43e-01 -0.10083 -2.02e-01 -2.02e-01 -2.02e-01 -3.81e-16 -4.43e-16
7  -1.53e-01  0.10841 -1.30e-01  1.19e-16  1.33e-16  1.59e-01  1.59e-01
8   2.23e-02 -0.01575 -9.45e-02  2.52e-18 -7.56e-18 -1.16e-01 -2.38e-17
9  -1.15e-01  0.08104  4.86e-01  3.31e-16  4.17e-16  0.00e+00  5.96e-01
10  3.07e-02 -0.02168 -1.30e-01  2.94e-17 -1.38e-17  7.97e-18 -6.29e-17
11  1.39e-02 -0.00984 -5.90e-02  4.90e-17  7.39e-17 -2.63e-17 -6.52e-17
12  1.39e-02 -0.00984 -5.90e-02 -1.44e-17 -2.55e-17 -5.98e-17 -6.48e-17
13 -9.74e-02  0.06890  9.18e-17 -8.27e-02  9.69e-17  1.01e-01  1.01e-01
14  7.90e-02 -0.05587  5.58e-17 -3.35e-01 -5.15e-17 -4.11e-01  1.39e-16
15 -5.60e-02  0.03962  1.06e-16  2.38e-01  1.49e-16  1.25e-16  2.91e-01
16 -1.39e-02  0.00984 -1.31e-17  5.90e-02  1.76e-17  1.81e-17  2.86e-17
17 -3.07e-02  0.02168 -5.78e-17  1.30e-01 -1.11e-16  9.02e-17  8.14e-17
18  2.78e-03 -0.00197  1.97e-18 -1.18e-02  8.45e-19 -8.12e-18 -7.67e-18
19  9.74e-02 -0.06890 -3.86e-17 -1.95e-17  8.27e-02 -1.01e-01 -1.01e-01
20 -9.66e-02  0.06831  1.65e-16  2.90e-16  4.10e-01  5.02e-01 -3.55e-16
21  1.46e-01 -0.10309 -5.84e-16 -6.19e-16 -6.19e-01 -3.91e-16 -7.58e-01
22  1.39e-02 -0.00984 -1.25e-17 -2.78e-17 -5.90e-02 -4.63e-17 -6.03e-17
23 -7.03e-02  0.04973 -2.14e-17  3.51e-17  2.98e-01  2.02e-16  2.18e-16
24  3.07e-02 -0.02168 -4.17e-17 -3.83e-17 -1.30e-01 -9.83e-17 -8.95e-17
25  6.43e-16 -0.88728 -5.57e-16 -5.38e-16 -5.43e-16  2.57e-16 -3.67e-16
26 -1.82e-16  0.14310 -9.32e-18  1.87e-17  4.86e-17  1.27e-16  1.37e-16
27  1.13e-16 -0.12491  3.54e-17  6.87e-18 -2.55e-17 -8.33e-17 -8.94e-17
28 -1.17e-16  0.14310  2.71e-17 -1.50e-17  4.86e-17 -4.04e-18  3.92e-17
29  4.50e-17 -0.07099 -9.57e-19 -2.51e-17 -7.24e-17  3.70e-18 -1.10e-17
30 -2.88e-16  0.19865  5.38e-17  1.33e-16  9.45e-17  7.11e-17  1.90e-16
31 -5.63e-16  0.47066  6.03e-16  3.33e-16  3.48e-16 -8.27e-17  5.78e-17
32  0.00e+00  0.13138 -1.64e-16  2.75e-17  1.37e-16 -1.83e-16  1.31e-16
33  2.36e-17  0.02168 -2.84e-17  2.26e-17  2.21e-17 -6.07e-17  1.17e-17
34  2.27e-16 -0.15172  2.17e-16 -1.83e-17 -8.88e-17 -5.87e-17 -3.13e-16
35  8.41e-17  0.10309 -1.40e-16  4.41e-18 -1.17e-17 -1.78e-16  7.74e-17
36 -5.62e-18 -0.01378  2.07e-17  1.71e-17  3.58e-18  5.65e-18 -2.02e-17
37  1.04e-16 -0.23851 -8.35e-17 -8.22e-17 -9.69e-17  1.56e-16 -1.34e-16
38 -7.08e-17  0.02366  5.63e-17  6.05e-17  3.75e-17  7.22e-17  2.64e-17
39  1.04e-17 -0.00590 -1.51e-17 -9.08e-18 -9.81e-18  5.61e-18 -1.09e-17
40  1.95e-17  0.04770  9.50e-17  9.69e-17  9.28e-17 -1.22e-16 -8.33e-17
41  1.49e-16 -0.15703 -3.96e-16 -2.09e-16 -1.96e-16  1.12e-16  3.89e-17
42 -2.42e-17  0.02962  1.03e-16  7.63e-17  6.88e-17 -2.26e-17 -2.45e-17
43 -8.45e-17  0.25886  9.42e-17  8.51e-17  4.22e-17 -2.02e-16  6.17e-17
44  2.10e-16 -0.10309 -1.54e-16 -2.67e-17 -1.26e-16 -2.39e-16 -1.18e-16
45  1.58e-17 -0.05792 -1.03e-16 -3.54e-17 -7.09e-17  1.01e-16  4.23e-17
46 -1.03e-16  0.15172  1.69e-16  9.28e-17  1.86e-16 -1.47e-16 -2.25e-17
47 -4.55e-17  0.01970  2.85e-17  1.21e-17  2.41e-17  1.54e-17  3.09e-17
48 -2.71e-17  0.04973  9.22e-17 -3.35e-18  8.12e-17 -1.55e-17 -9.05e-18
    dfb.blIV  dfb.blqV  dfb.blVI  dfb.lP.2  dfb.lP.3  dfb.lP.4 dfb.lgP.II
1  -1.59e-01 -1.59e-01 -1.59e-01  9.20e-02  9.20e-02  9.20e-02   1.13e-01
2   1.59e-17  2.23e-17  2.30e-17  1.67e-02  1.67e-02  1.67e-02  -2.04e-02
3   1.50e-16  1.26e-16  1.17e-16 -8.36e-02 -8.36e-02 -8.36e-02  -2.03e-16
4   1.59e-01 -2.12e-16 -2.42e-16  9.20e-02  9.20e-02  9.20e-02   2.40e-16
5   5.99e-16 -4.56e-01  6.32e-16 -2.63e-01 -2.63e-01 -2.63e-01  -6.44e-16
6  -2.74e-16 -2.85e-16  2.47e-01  1.43e-01  1.43e-01  1.43e-01   3.80e-16
7   1.59e-01  1.59e-01  1.59e-01  9.20e-02 -1.70e-16 -1.68e-16  -1.13e-01
8  -1.52e-17 -1.36e-18  6.69e-20  6.68e-02 -2.90e-17 -1.36e-17   8.19e-02
9   2.60e-17 -6.96e-17  2.26e-16 -3.44e-01 -2.92e-16 -4.18e-16  -1.27e-16
10 -1.59e-01 -2.47e-17  3.69e-17  9.20e-02  3.21e-17  1.41e-17  -1.72e-17
11 -1.97e-17 -7.23e-02 -3.19e-17  4.17e-02 -4.00e-17 -5.11e-17   1.94e-17
12 -4.57e-17 -4.87e-17 -7.23e-02  4.17e-02  2.60e-17  3.90e-17   8.94e-17
13  1.01e-01  1.01e-01  1.01e-01 -1.20e-16  5.85e-02 -1.21e-16  -7.16e-02
14  1.79e-16  1.47e-16  7.24e-17 -1.05e-16  2.37e-01 -1.36e-31   2.90e-01
15  2.34e-16  1.75e-16  1.20e-16 -1.87e-16 -1.68e-01 -1.36e-16  -1.15e-16
16  7.23e-02  1.72e-17  2.58e-17 -4.63e-18 -4.17e-02 -2.48e-17   7.90e-18
17  1.30e-16  1.59e-01  6.45e-17  1.02e-17 -9.20e-02  3.44e-17  -5.40e-17
18 -1.50e-17 -5.56e-18 -1.45e-02 -9.26e-19  8.34e-03 -1.42e-19   7.20e-18
19 -1.01e-01 -1.01e-01 -1.01e-01  9.89e-17  8.26e-17 -5.85e-02   7.16e-02
20 -5.04e-16 -4.81e-16 -3.14e-16 -1.95e-18 -1.02e-16 -2.90e-01  -3.55e-01
21 -4.07e-16 -3.45e-16 -4.66e-16  5.64e-16  3.09e-16  4.37e-01   3.69e-16
22 -7.23e-02 -3.61e-17 -7.16e-17  1.64e-17  4.92e-17  4.17e-02   2.83e-17
23  1.66e-16  3.65e-01  8.54e-17 -7.24e-17 -1.12e-16 -2.11e-01  -1.09e-16
24 -1.16e-16 -4.60e-17 -1.59e-01  2.40e-17  1.08e-17  9.20e-02   9.14e-17
25 -2.18e-17 -1.39e-16 -4.48e-17  4.18e-01  4.18e-01  4.18e-01   5.12e-01
26  1.77e-16  1.49e-16  1.64e-16 -2.02e-01 -2.02e-01 -2.02e-01   2.48e-01
27 -8.55e-17 -1.37e-16 -9.91e-17  1.77e-01  1.77e-01  1.77e-01   8.37e-17
28 -4.56e-18  4.91e-17  4.05e-17 -2.02e-01 -2.02e-01 -2.02e-01   2.98e-17
29 -4.89e-18  3.01e-19 -1.89e-17  1.00e-01  1.00e-01  1.00e-01   1.52e-17
30  1.25e-16  2.26e-16  2.25e-16 -2.81e-01 -2.81e-01 -2.81e-01  -5.47e-17
31  2.21e-16  1.22e-16 -2.12e-17  3.99e-01 -2.00e-16 -2.88e-16  -4.89e-01
32 -2.21e-16  3.59e-17  1.07e-16 -5.57e-01  2.46e-17 -1.23e-16  -6.83e-01
33 -5.55e-17 -4.42e-17 -2.14e-17 -9.20e-02 -2.40e-17 -1.95e-17   5.81e-17
34 -4.80e-16 -1.58e-16 -2.22e-16  6.44e-01 -3.02e-17  4.38e-17   2.77e-17
35 -1.62e-16 -3.00e-17 -9.64e-17 -4.37e-01  2.18e-17  3.72e-17   2.16e-16
36  2.76e-18  7.44e-19 -1.31e-17  5.85e-02 -2.85e-17 -7.95e-18  -7.39e-18
37  3.09e-17  5.17e-17  9.51e-17  8.99e-17 -2.02e-01  7.05e-17   2.48e-01
38 -2.30e-18  2.97e-17  1.76e-17 -2.79e-17 -1.00e-01 -2.22e-17  -1.23e-01
39 -4.22e-19 -4.21e-19  2.01e-19  8.34e-18  2.50e-02  6.17e-18  -3.96e-18
40 -1.44e-16 -4.88e-17 -8.92e-17 -3.37e-17 -2.02e-01 -6.88e-17   1.11e-16
41  2.86e-17 -8.18e-17  1.41e-16  2.59e-16  6.66e-01  1.25e-16  -1.38e-16
42 -6.25e-18 -4.09e-17 -7.65e-17 -7.67e-17 -1.26e-01 -6.84e-17   1.40e-17
43 -4.30e-17 -3.13e-17 -9.61e-17 -1.06e-16 -2.59e-17  2.20e-01  -2.69e-01
44 -1.08e-16 -9.35e-17 -6.26e-17  7.14e-17 -7.73e-17  4.37e-01   5.36e-01
45  1.50e-17  5.77e-17  2.17e-17  6.82e-17  0.00e+00  2.46e-01  -1.29e-16
46  1.16e-16 -8.21e-17 -2.58e-17 -3.57e-17  0.00e+00 -6.44e-01   1.29e-16
47  3.34e-17  7.46e-17  1.57e-17 -2.02e-17 -4.92e-18 -8.36e-02  -1.58e-17
48  2.02e-17 -3.44e-17 -5.41e-17 -6.96e-17  3.73e-17 -2.11e-01  -5.54e-18
   dfb.lP.III dfb.lP.IV dfb.lgP.V dfb.lP.VI   dffit  cov.r   cook.d   hat inf
1    1.13e-01  1.13e-01  1.13e-01  1.13e-01  0.2760 2.7227 0.004358 0.375    
2   -3.31e-17 -3.42e-17 -4.45e-17 -4.14e-17  0.0501 2.9377 0.000144 0.375   *
3    1.02e-01 -1.66e-16 -1.66e-16 -1.34e-16 -0.2508 2.7601 0.003602 0.375    
4    2.32e-16 -1.13e-01  1.87e-16  2.00e-16  0.2760 2.7227 0.004358 0.375    
5   -6.27e-16 -5.85e-16  3.22e-01 -5.64e-16 -0.7898 1.5623 0.034612 0.375    
6    3.95e-16  2.49e-16  3.19e-16 -1.75e-01  0.4278 2.4397 0.010409 0.375    
7   -1.13e-01 -1.13e-01 -1.13e-01 -1.13e-01 -0.2760 2.7227 0.004358 0.375    
8   -1.97e-17  1.06e-17 -6.62e-17 -7.72e-17 -0.2005 2.8255 0.002305 0.375   *
9   -4.21e-01 -9.33e-17 -1.37e-17 -2.81e-16  1.0315 1.0119 0.057627 0.375    
10   5.93e-17  1.13e-01  4.30e-17 -2.50e-17 -0.2760 2.7227 0.004358 0.375    
11   5.23e-17  1.16e-17  5.11e-02  3.55e-17 -0.1252 2.8980 0.000900 0.375   *
12   7.83e-17  5.67e-17  5.90e-17  5.11e-02 -0.1252 2.8980 0.000900 0.375   *
13  -7.16e-02 -7.16e-02 -7.16e-02 -7.16e-02 -0.1754 2.8532 0.001765 0.375   *
14  -1.34e-16 -1.72e-16 -9.10e-17 -5.64e-17 -0.7111 1.7588 0.028237 0.375    
15  -2.06e-01 -2.10e-16 -1.91e-16 -8.57e-17  0.5043 2.2683 0.014407 0.375    
16  -4.49e-18 -5.11e-02 -3.55e-18 -7.09e-18  0.1252 2.8980 0.000900 0.375   *
17  -3.29e-17 -9.19e-17 -1.13e-01 -5.00e-17  0.2760 2.7227 0.004358 0.375    
18   5.20e-18  1.15e-17  3.93e-18  1.02e-02 -0.0250 2.9435 0.000036 0.375   *
19   7.16e-02  7.16e-02  7.16e-02  7.16e-02  0.1754 2.8532 0.001765 0.375   *
20   4.11e-16  4.86e-16  4.27e-16  3.25e-16  0.8694 1.3699 0.041635 0.375    
21   5.36e-01  4.55e-16  4.75e-16  4.61e-16 -1.3122 0.5389 0.090041 0.375    
22   4.26e-17  5.11e-02  4.09e-17  6.95e-17 -0.1252 2.8980 0.000900 0.375   *
23  -1.06e-16 -1.05e-16 -2.58e-01 -5.02e-17  0.6330 1.9550 0.022510 0.375    
24   7.46e-17  1.08e-16  3.25e-17  1.13e-01 -0.2760 2.7227 0.004358 0.375    
25   5.12e-01  5.12e-01  5.12e-01  5.12e-01 -1.2548 0.6194 0.082982 0.375    
26  -1.13e-16 -1.07e-16 -1.10e-16 -1.31e-16  0.6071 2.0196 0.020746 0.375    
27  -2.16e-01  5.09e-17  7.36e-17  9.01e-17 -0.5299 2.2079 0.015883 0.375    
28  -1.09e-17  2.48e-01 -1.33e-17 -2.06e-17  0.6071 2.0196 0.020746 0.375    
29   1.76e-17  5.57e-18 -1.23e-01  1.71e-17 -0.3012 2.6822 0.005186 0.375    
30  -1.57e-16 -6.62e-17 -1.98e-16  3.44e-01  0.8428 1.4334 0.039222 0.375    
31  -4.89e-01 -4.89e-01 -4.89e-01 -4.89e-01  1.1981 0.7070 0.076211 0.375    
32   2.14e-17  1.09e-16  2.65e-17 -9.47e-17 -1.6722 0.2015 0.138448 0.375    
33  -1.13e-01  4.12e-17  3.67e-17  2.19e-17 -0.2760 2.7227 0.004358 0.375    
34   1.38e-16  7.88e-01  4.52e-17  1.09e-16  1.9310 0.0894 0.176481 0.375    
35   1.29e-17  1.46e-16 -5.36e-01  1.64e-16 -1.3122 0.5389 0.090041 0.375    
36   1.19e-17  4.20e-18 -6.88e-18  7.16e-02  0.1754 2.8532 0.001765 0.375   *
37   2.48e-01  2.48e-01  2.48e-01  2.48e-01 -0.6071 2.0196 0.020746 0.375    
38  -7.52e-18  2.34e-18 -2.09e-17 -3.41e-18 -0.3012 2.6822 0.005186 0.375    
39   3.07e-02  4.47e-19  5.84e-18 -8.51e-19  0.0751 2.9282 0.000324 0.375   *
40   7.61e-17 -2.48e-01  4.27e-17  1.03e-16 -0.6071 2.0196 0.020746 0.375    
41  -9.01e-17 -7.40e-17  8.16e-01 -2.04e-16  1.9986 0.0714 0.186710 0.375    
42   2.48e-17  8.46e-19  4.44e-17 -1.54e-01 -0.3770 2.5441 0.008104 0.375    
43  -2.69e-01 -2.69e-01 -2.69e-01 -2.69e-01  0.6589 1.8900 0.024347 0.375    
44   1.36e-16  2.13e-16  8.22e-17  7.43e-17  1.3122 0.5389 0.090041 0.375    
45   3.01e-01 -3.99e-17 -7.01e-17 -7.52e-17  0.7372 1.6931 0.030290 0.375    
46  -3.46e-17 -7.88e-01  2.00e-16  1.53e-16 -1.9310 0.0894 0.176481 0.375    
47  -3.74e-17 -4.18e-17 -1.02e-01 -1.42e-17 -0.2508 2.7601 0.003602 0.375    
48  -2.37e-17 -5.37e-17  4.97e-17 -2.58e-01 -0.6330 1.9550 0.022510 0.375    
influenceIndexPlot(modelo.dbca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dbca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1     -0.28504862      2.553305  0.3736
   2     -0.11122366      2.203314  0.8720
   3      0.15768504      1.552944  0.0844
   4     -0.09049163      2.027643  0.6740
   5     -0.14390870      2.056569  0.3884
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dbca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dbca
DW = 2.5533, p-value = 0.3762
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.dbca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dbca)
W = 0.97797, p-value = 0.497
ad.test(rstudent(modelo.dbca))

    Anderson-Darling normality test

data:  rstudent(modelo.dbca)
A = 0.44887, p-value = 0.2665
lillie.test(rstudent(modelo.dbca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dbca)
D = 0.10527, p-value = 0.2024
ks.test(rstudent(modelo.dbca), "pnorm",
        alternative = "two.sided")

    Exact one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dbca)
D = 0.098701, p-value = 0.7009
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dbca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dbca)
W = 0.07727, p-value = 0.2195
pearson.test(rstudent(modelo.dbca))

    Pearson chi-square normality test

data:  rstudent(modelo.dbca)
P = 6.1667, p-value = 0.5204
sf.test(rstudent(modelo.dbca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dbca)
W = 0.97561, p-value = 0.3478

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dbca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 11.05181, Df = 1, p = 0.00088601
bptest(modelo.dbca)

    studentized Breusch-Pagan test

data:  modelo.dbca
BP = 22.771, df = 17, p-value = 0.1568
bptest(modelo.dbca, studentize = F)

    Breusch-Pagan test

data:  modelo.dbca
BP = 24.273, df = 17, p-value = 0.1122
olsrr::ols_test_breusch_pagan(modelo.dbca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

              Data               
 --------------------------------
 Response : rdto 
 Variables: fitted values of rdto 

         Test Summary           
 -------------------------------
 DF            =    1 
 Chi2          =    11.05181 
 Prob > Chi2   =    0.0008860059 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dbca %>% gvlma()

Call:
lm(formula = rdto ~ lugar * linaje + bloque %in% lugar + bloque, 
    data = data_D)

Coefficients:
         (Intercept)            lugarPisco               linaje2  
             11.0833                1.9167               -0.1667  
             linaje3               linaje4              bloqueII  
             -1.5000               -3.6667                1.7500  
           bloqueIII              bloqueIV               bloqueV  
              0.7500                1.0000                2.5000  
            bloqueVI    lugarPisco:linaje2    lugarPisco:linaje3  
              2.5000                2.3333                2.5000  
  lugarPisco:linaje4   lugarPisco:bloqueII  lugarPisco:bloqueIII  
              3.5000                1.2500               -1.0000  
 lugarPisco:bloqueIV    lugarPisco:bloqueV   lugarPisco:bloqueVI  
              4.0000               -0.5000               -1.2500  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                       Value  p-value                   Decision
Global Stat        7.6911887 0.103568    Assumptions acceptable.
Skewness           0.0622679 0.802947    Assumptions acceptable.
Kurtosis           0.0347871 0.852043    Assumptions acceptable.
Link Function      0.0003691 0.984673    Assumptions acceptable.
Heteroscedasticity 7.5937648 0.005857 Assumptions NOT satisfied!

Análisis de varianza

\[Y_{ijk} = \mu + \tau_{i} + \text{Error}(\tau\text{Bloque})_{i(k)} + \beta_{j} + (\tau\beta)_{ij} + \gamma_{k} + \epsilon_{ijk}\]

\[\hat{Y}_{ijk} = \mu + \tau_{i} + \text{Error}(\tau\text{Bloque})_{i(k)} + \beta_{j} + (\tau\beta)_{ij} + \gamma_{k}\]

Dónde:

\(Y_{ijk}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijk}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor lugar.

\(\text{Error}(\tau\text{Bloque})_{i(k)}\) = Efecto del i-ésimo nivel de lugar en el l-ésimo nivel de Bloque.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor tratamiento (linaje).

\((\tau\beta)_{ij}\) = Efecto de la interacción entre el i-ésimo nivel del factor lugar y el j-ésimo nivel del factor linaje.

\(\gamma_{k}\) = Efecto del k-ésimo nivel de Bloque.

\(\epsilon_{ijk}\) = Residuo observado del modelo.

Pruebas de hipótesis

Para el factor A (lugar):

\(H_0: \tau_{A1} = \tau_{A2} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (linaje):

\(H_0: \beta_{B1} = \beta_{B2} = \beta_{B3} = \beta_{B4} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dbca, test = "F")
Analysis of Variance Table

Response: rdto
             Df  Sum Sq Mean Sq F value    Pr(>F)    
lugar         1 234.083 234.083 22.7634 4.443e-05 ***
linaje        3  52.750  17.583  1.7099    0.1861    
bloque        5  59.500  11.900  1.1572    0.3529    
lugar:linaje  3  19.750   6.583  0.6402    0.5951    
lugar:bloque  5  38.667   7.733  0.7520    0.5912    
Residuals    30 308.500  10.283                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
GAD::estimates(modelo.dbca)
$tm
             lugar linaje bloque        n
lugar            0      4      6 2.666667
linaje           2      0      6 2.666667
bloque           2      4      1 2.666667
lugar:linaje     0      0      6 2.666667
lugar:bloque     0      4      1 2.666667
Res              1      1      1 1.000000

$mse
             Mean square estimates       
lugar        "Res + lugar:bloque + lugar"
linaje       "Res + linaje"              
bloque       "Res + bloque"              
lugar:linaje "Res + lugar:linaje"        
lugar:bloque "Res + lugar:bloque"        
Residual     "Res"                       

$f.versus
             F-ratio versus
lugar        "lugar:bloque"
linaje       "Residual"    
bloque       "Residual"    
lugar:linaje "Residual"    
lugar:bloque "Residual"    
GAD::gad(modelo.dbca)
Analysis of Variance Table

Response: rdto
             Df  Sum Sq Mean Sq F value   Pr(>F)   
lugar         1 234.083 234.083 30.2694 0.002711 **
linaje        3  52.750  17.583  1.7099 0.186072   
bloque        5  59.500  11.900  1.1572 0.352864   
lugar:linaje  3  19.750   6.583  0.6402 0.595111   
lugar:bloque  5  38.667   7.733  0.7520 0.591194   
Residual     30 308.500  10.283                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(Zona/Bloque)” en el caso de efectos aleatorios o “Error(Zona:Bloque)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos.

aov(rdto ~ bloque + lugar * linaje + Error(bloque %in% lugar) + bloque, data = data_D) -> aov.dbca
summary(aov.dbca)

Error: bloque:lugar
          Df Sum Sq Mean Sq F value  Pr(>F)   
bloque     5  59.50   11.90   1.539 0.32389   
lugar      1 234.08  234.08  30.269 0.00271 **
Residuals  5  38.67    7.73                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Error: Within
             Df Sum Sq Mean Sq F value Pr(>F)
linaje        3  52.75  17.583    1.71  0.186
lugar:linaje  3  19.75   6.583    0.64  0.595
Residuals    30 308.50  10.283               
broom::tidy(aov.dbca)
# A tibble: 6 × 7
  stratum      term            df sumsq meansq statistic  p.value
  <chr>        <chr>        <dbl> <dbl>  <dbl>     <dbl>    <dbl>
1 bloque:lugar bloque           5  59.5  11.9      1.54   0.324  
2 bloque:lugar lugar            1 234.  234.      30.3    0.00271
3 bloque:lugar Residuals        5  38.7   7.73    NA     NA      
4 Within       linaje           3  52.7  17.6      1.71   0.186  
5 Within       lugar:linaje     3  19.8   6.58     0.640  0.595  
6 Within       Residuals       30 308.   10.3     NA     NA      
broom::tidy(gad(modelo.dbca))
# A tibble: 6 × 6
  term            df sumsq meansq statistic  p.value
  <chr>        <int> <dbl>  <dbl>     <dbl>    <dbl>
1 lugar            1 234.  234.      30.3    0.00271
2 linaje           3  52.7  17.6      1.71   0.186  
3 bloque           5  59.5  11.9      1.16   0.353  
4 lugar:linaje     3  19.7   6.58     0.640  0.595  
5 lugar:bloque     5  38.7   7.73     0.752  0.591  
6 Residual        30 308.   10.3     NA     NA      

Valor de la tabla de F para el factor lugar con una significancia de 0.05.

qf(0.95, 1, 5)
[1] 6.607891

Valor de la tabla de F para el factor linaje con una significancia de 0.05.

qf(0.95, 3, 30)
[1] 2.922277

Conclusión.

Con respecto al Factor lugar: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor lugar tienen un efecto sobre el rendimiento estadísticamente diferente a 0.

Con respecto al Factor linaje: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor linaje tienen un efecto sobre el rendimiento estadísticamente similar a 0.

agricolae::cv.model(modelo.dbca)
[1] 23.9758

Comparaciones de medias para los efectos principales del Factor Lugar

get_df_ea(aov.dbca)
[1] 5
get_mse_ea(aov.dbca)
[1] 7.733333
data_D %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  lugar, # Cambiar según nombre de variable independiente
  DFerror = get_df_ea(aov.dbca), 
  MSerror = get_mse_ea(aov.dbca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ lugar

LSD t Test for rdto 

Mean Square Error:  7.733333 

lugar,  means and individual ( 95 %) CI

          rdto      std  r       LCL      UCL Min Max
Lima  11.16667 2.443566 24  9.707486 12.62585   4  15
Pisco 15.58333 3.855168 24 14.124152 17.04251   9  26

Alpha: 0.05 ; DF Error: 5
Critical Value of t: 2.570582 

least Significant Difference: 2.063594 

Treatments with the same letter are not significantly different.

          rdto groups
Pisco 15.58333      a
Lima  11.16667      b

Comparaciones de medias para los efectos principales del Factor Linaje

data_D %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  linaje, # Cambiar según nombre de variable independiente
  DFerror = df.residual(modelo.dbca), 
  MSerror = dvmisc::get_mse(modelo.dbca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ linaje

LSD t Test for rdto 

Mean Square Error:  10.28333 

linaje,  means and individual ( 95 %) CI

      rdto      std  r       LCL      UCL Min Max
1 13.66667 3.284491 12 11.776109 15.55722   9  20
2 14.66667 4.334499 12 12.776109 16.55722  10  26
3 13.41667 3.629634 12 11.526109 15.30722   9  22
4 11.75000 4.158780 12  9.859442 13.64056   4  20

Alpha: 0.05 ; DF Error: 30
Critical Value of t: 2.042272 

least Significant Difference: 2.673653 

Treatments with the same letter are not significantly different.

      rdto groups
2 14.66667      a
1 13.66667     ab
3 13.41667     ab
4 11.75000      b

Análisis de DBCA de dos vías con análisis combinado en un sitio


Importación de datos


data_D <- data %>%
  dplyr::filter(lugar %in% "Lima")

Definición del modelo


modelo.dbca <- lm(rdto ~ epoca * linaje + bloque %in% epoca + bloque, data = data_D)
summary(modelo.dbca)

Call:
lm(formula = rdto ~ epoca * linaje + bloque %in% epoca + bloque, 
    data = data_D)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.1667 -0.9271 -0.1042  0.9271  5.3750 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)       1.108e+01  1.562e+00   7.097 6.83e-08 ***
epoca2            5.125e+00  2.209e+00   2.320   0.0273 *  
linaje2          -1.667e-01  1.472e+00  -0.113   0.9106    
linaje3          -1.500e+00  1.472e+00  -1.019   0.3165    
linaje4          -3.667e+00  1.472e+00  -2.490   0.0185 *  
bloqueII          1.750e+00  1.803e+00   0.970   0.3396    
bloqueIII         7.500e-01  1.803e+00   0.416   0.6804    
bloqueIV          1.000e+00  1.803e+00   0.555   0.5833    
bloqueV           2.500e+00  1.803e+00   1.386   0.1759    
bloqueVI          2.500e+00  1.803e+00   1.386   0.1759    
epoca2:linaje2   -1.167e+00  2.082e+00  -0.560   0.5795    
epoca2:linaje3   -3.833e+00  2.082e+00  -1.841   0.0755 .  
epoca2:linaje4   -3.500e+00  2.082e+00  -1.681   0.1032    
epoca2:bloqueII   1.250e+00  2.550e+00   0.490   0.6276    
epoca2:bloqueIII  1.000e+00  2.550e+00   0.392   0.6978    
epoca2:bloqueIV  -9.971e-16  2.550e+00   0.000   1.0000    
epoca2:bloqueV    7.500e-01  2.550e+00   0.294   0.7707    
epoca2:bloqueVI   3.250e+00  2.550e+00   1.274   0.2123    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.55 on 30 degrees of freedom
Multiple R-squared:  0.7389,    Adjusted R-squared:  0.5909 
F-statistic: 4.994 on 17 and 30 DF,  p-value: 6.425e-05

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dbca)
ggResidpanel::resid_panel(modelo.dbca)
influence.measures(modelo.dbca)
Influence measures of
     lm(formula = rdto ~ epoca * linaje + bloque %in% epoca + bloque,      data = data_D) :

      dfb.1_ dfb.epc2  dfb.lnj2  dfb.lnj3  dfb.lnj4  dfb.blII  dfb.bIII
1   3.47e-01 -0.24568 -1.64e-01 -1.64e-01 -1.64e-01 -2.01e-01 -2.01e-01
2   2.10e-02 -0.01484 -2.97e-02 -2.97e-02 -2.97e-02  3.64e-02 -1.04e-17
3  -1.05e-01  0.07440  1.49e-01  1.49e-01  1.49e-01  2.59e-16 -1.82e-01
4   1.16e-01 -0.08189 -1.64e-01 -1.64e-01 -1.64e-01 -2.80e-16 -2.38e-16
5  -3.35e-01  0.23656  4.73e-01  4.73e-01  4.73e-01  1.63e-16  1.85e-16
6   1.80e-01 -0.12718 -2.54e-01 -2.54e-01 -2.54e-01 -1.57e-16 -4.67e-16
7   5.10e-16 -0.32469 -1.44e-16 -1.80e-16 -2.53e-16  4.98e-17 -7.58e-17
8   8.33e-17  0.07066 -6.57e-17 -6.63e-17 -3.68e-17 -2.29e-16 -5.64e-17
9   0.00e+00 -0.08564  2.30e-17  3.47e-18 -4.85e-17  1.96e-16  5.61e-19
10 -1.09e-16  0.07066  4.20e-17  3.78e-17  8.81e-17 -8.24e-17  3.92e-17
11  1.26e-16 -0.04084 -1.43e-17 -3.83e-17 -4.54e-17 -2.41e-18 -7.67e-17
12 -2.45e-16  0.09316  7.26e-17  8.91e-17  1.29e-16 -5.46e-17  9.94e-17
13 -1.93e-01  0.13649 -1.64e-01  2.67e-16  3.61e-16  2.01e-01  2.01e-01
14  2.80e-02 -0.01982 -1.19e-01 -1.03e-17 -3.73e-17 -1.46e-01  5.17e-18
15 -1.47e-01  0.10376  6.23e-01  7.58e-16  6.51e-16  0.00e+00  7.63e-01
16  3.86e-02 -0.02730 -1.64e-01  2.30e-17 -3.76e-17 -1.76e-17 -8.80e-17
17  1.75e-02 -0.01237 -7.42e-02 -2.19e-17 -2.40e-17  3.11e-18 -3.99e-18
18  1.75e-02 -0.01237 -7.42e-02 -2.01e-17 -3.03e-17  9.47e-18 -4.49e-17
19  1.98e-16 -0.13025 -1.62e-16 -9.90e-17 -9.97e-17 -1.29e-16 -3.39e-17
20  3.07e-17  0.05646 -2.28e-16 -2.29e-17 -4.06e-17 -8.22e-17  9.50e-17
21  4.54e-18 -0.01114  2.41e-17 -6.50e-18 -1.02e-17  3.10e-17  6.96e-19
22 -9.21e-17  0.05646 -1.59e-16 -9.07e-18 -1.72e-17 -9.60e-17  1.94e-16
23 -6.39e-17  0.03356 -8.65e-17  3.98e-17  3.61e-17 -4.41e-17  1.01e-16
24  3.48e-16 -0.18260  5.07e-16  9.79e-17 -3.80e-17  2.74e-16 -7.10e-16
25 -1.23e-01  0.08668  1.96e-16 -1.04e-01  2.56e-16  1.27e-01  1.27e-01
26  1.00e-01 -0.07085  2.36e-16 -4.25e-01  2.08e-17 -5.21e-01 -6.35e-17
27 -7.08e-02  0.05003  3.33e-16  3.00e-01  2.51e-16  1.90e-16  3.68e-01
28 -1.75e-02  0.01237 -8.24e-18  7.42e-02 -2.30e-18  2.39e-18  1.20e-17
29 -3.86e-02  0.02730  2.73e-17  1.64e-01  4.76e-18  5.11e-17  3.78e-17
30  3.50e-03 -0.00247 -4.12e-18 -1.48e-02 -2.20e-18  1.88e-18 -6.64e-18
31 -4.89e-16  0.32132  1.50e-16  2.24e-16  1.30e-16  2.75e-16  3.01e-16
32 -3.60e-17  0.08837 -3.71e-17 -9.70e-17  1.18e-16  1.75e-16 -8.25e-17
33  1.54e-16 -0.14141 -8.31e-17 -6.36e-17 -3.27e-16  2.71e-16  2.32e-16
34  3.03e-18 -0.00371 -4.52e-18 -2.41e-18 -7.44e-18  6.95e-18  1.25e-18
35 -1.16e-17  0.00371  2.11e-18  4.58e-18  9.16e-18  8.04e-19  4.96e-18
36 -1.55e-16  0.11389  1.16e-16  1.70e-17  2.75e-16 -1.86e-16  8.40e-17
37  1.23e-01 -0.08668 -1.41e-16 -1.29e-16  1.04e-01 -1.27e-01 -1.27e-01
38 -1.23e-01  0.08700 -5.44e-17  1.84e-16  5.22e-01  6.39e-01  8.17e-18
39  1.89e-01 -0.13352 -1.18e-15 -1.27e-15 -8.01e-01 -5.06e-16 -9.81e-01
40  1.75e-02 -0.01237 -2.09e-17 -1.31e-17 -7.42e-02 -2.59e-17 -3.19e-17
41 -8.90e-02  0.06296  1.93e-16  2.00e-16  3.78e-01  1.50e-16  3.99e-17
42  3.86e-02 -0.02730 -1.26e-16 -1.06e-16 -1.64e-01 -2.33e-17 -8.82e-17
43  8.07e-18 -0.00618 -3.11e-18 -3.95e-18 -3.53e-18 -2.71e-18 -5.49e-18
44 -5.13e-17 -0.12583 -5.13e-17 -5.13e-17 -1.03e-16  3.09e-17  1.95e-16
45 -3.10e-16  0.11981  2.31e-16  3.01e-16  3.91e-16  2.26e-17  9.49e-17
46  7.76e-18 -0.02855 -2.74e-17 -2.41e-17 -5.82e-17  2.58e-17  2.58e-17
47  1.40e-16 -0.05132 -4.57e-17 -6.28e-17 -1.26e-16 -8.67e-17 -6.24e-17
48 -2.45e-16  0.08563  7.82e-17  9.36e-18  1.40e-16  1.52e-16  1.74e-16
    dfb.blIV  dfb.blqV  dfb.blVI  dfb.e2.2  dfb.e2.3  dfb.e2.4 dfb.ep2.II
1  -2.01e-01 -2.01e-01 -2.01e-01  1.16e-01  1.16e-01  1.16e-01   1.42e-01
2   1.59e-17  6.23e-18 -8.66e-18  2.10e-02  2.10e-02  2.10e-02  -2.57e-02
3   2.24e-16  2.31e-16  2.01e-16 -1.05e-01 -1.05e-01 -1.05e-01  -1.72e-16
4   2.01e-01 -2.42e-16 -1.86e-16  1.16e-01  1.16e-01  1.16e-01   2.19e-16
5   1.31e-16 -5.79e-01  1.30e-16 -3.35e-01 -3.35e-01 -3.35e-01  -3.13e-16
6  -3.60e-16 -3.59e-16  3.12e-01  1.80e-01  1.80e-01  1.80e-01   6.67e-17
7  -1.23e-16 -1.74e-16 -1.39e-16  1.53e-01  1.53e-01  1.53e-01   1.87e-01
8  -1.45e-16 -1.46e-16 -7.89e-17 -9.99e-02 -9.99e-02 -9.99e-02   1.22e-01
9   5.33e-17  7.80e-17  1.35e-16  1.21e-01  1.21e-01  1.21e-01  -2.10e-16
10  2.26e-17  6.62e-18  1.60e-17 -9.99e-02 -9.99e-02 -9.99e-02   6.94e-17
11 -6.76e-17 -4.98e-17 -7.24e-17  5.78e-02  5.78e-02  5.78e-02   2.43e-17
12  1.01e-16  7.52e-17  1.54e-16 -1.32e-01 -1.32e-01 -1.32e-01   2.46e-17
13  2.01e-01  2.01e-01  2.01e-01  1.16e-01 -2.51e-16 -3.08e-16  -1.42e-01
14  4.18e-17  4.12e-17  6.77e-17  8.41e-02 -5.05e-17 -1.43e-17   1.03e-01
15 -1.92e-17  2.92e-17  1.16e-16 -4.40e-01 -5.40e-16 -5.09e-16  -9.27e-17
16 -2.01e-01 -1.48e-16 -1.50e-16  1.16e-01  8.30e-17  9.45e-17   5.54e-17
17  0.00e+00 -9.09e-02 -5.68e-18  5.25e-02  1.37e-17  5.80e-18   1.49e-17
18 -4.88e-17 -3.50e-17 -9.09e-02  5.25e-02  1.98e-17  3.03e-17   6.44e-18
19 -5.11e-17 -5.06e-17 -4.52e-17 -1.11e-01  6.09e-17  8.92e-17   1.35e-01
20 -1.28e-16 -2.57e-17 -5.47e-17 -2.40e-01  2.40e-17  6.92e-17  -2.93e-01
21  4.04e-18 -1.01e-18  4.54e-18  4.72e-02  8.00e-18  1.04e-17  -4.98e-18
22  9.91e-17  6.42e-17  4.03e-17 -2.40e-01  1.89e-17  4.48e-17   9.55e-17
23  1.60e-17  3.54e-17  1.54e-17 -1.42e-01 -5.92e-17 -4.72e-17   2.48e-17
24 -2.09e-16 -3.27e-16 -2.23e-16  7.75e-01 -1.06e-16  3.95e-17  -3.40e-16
25  1.27e-01  1.27e-01  1.27e-01 -1.84e-16  7.35e-02 -2.21e-16  -9.01e-02
26  3.48e-17  9.90e-17  2.25e-16 -4.34e-16  3.01e-01 -2.15e-16   3.68e-01
27  1.59e-16  1.44e-16  2.47e-16 -3.65e-16 -2.12e-01 -1.95e-16  -2.68e-16
28  9.09e-02  1.85e-17  3.45e-17 -2.33e-17 -5.25e-02 -2.50e-17   4.97e-18
29  4.55e-17  2.01e-01  6.91e-17 -1.93e-17 -1.16e-01  3.44e-17  -6.14e-17
30 -7.41e-18  0.00e+00 -1.82e-02  4.08e-18  1.05e-02  2.50e-18   1.32e-18
31  1.25e-16  2.87e-16  1.55e-16 -1.06e-16  2.73e-01 -1.37e-16  -3.34e-01
32 -1.55e-16 -5.95e-17 -8.26e-17  1.25e-16 -3.75e-01 -3.82e-17  -4.59e-01
33 -6.13e-17  4.59e-17 -9.13e-17  0.00e+00  6.00e-01  2.35e-16   3.16e-17
34  4.14e-18 -5.58e-19  6.31e-19  3.49e-18  1.57e-02  4.55e-18  -6.31e-18
35  8.37e-18  1.11e-17  5.99e-18  0.00e+00 -1.57e-02 -7.89e-18  -3.25e-18
36  7.15e-18 -2.56e-18  6.19e-17 -8.05e-17 -4.83e-01 -2.38e-16   2.34e-16
37 -1.27e-01 -1.27e-01 -1.27e-01  1.49e-16  1.52e-16 -7.35e-02   9.01e-02
38 -1.92e-16 -1.75e-16 -2.94e-16  4.63e-16  2.83e-16 -3.69e-01  -4.52e-01
39 -2.22e-16 -2.31e-16 -5.49e-16  1.13e-15  7.34e-16  5.66e-01   8.35e-16
40 -9.09e-02 -3.28e-17 -5.72e-17  2.78e-17  3.09e-17  5.25e-02   2.78e-17
41 -8.39e-17  4.63e-01  6.96e-17 -8.46e-17 -3.15e-17 -2.67e-01  -2.20e-16
42 -5.19e-17 -1.93e-17 -2.01e-01  1.13e-16  6.82e-17  1.16e-01   8.12e-17
43 -1.20e-18 -5.57e-18 -3.24e-18  2.47e-18  2.16e-18 -5.25e-03   6.43e-03
44  1.82e-16  1.93e-16  1.82e-16 -4.88e-17  3.14e-17  5.34e-01   6.54e-01
45  1.66e-16  1.08e-16  2.85e-17 -2.33e-16 -3.59e-16 -5.08e-01  -1.61e-16
46  5.55e-17  2.54e-17  2.23e-17  2.06e-17  2.14e-17  1.21e-01  -3.58e-17
47 -9.87e-17 -7.85e-17 -7.24e-17  4.20e-17  8.97e-17  2.18e-01   9.78e-17
48  2.39e-16  1.42e-16  2.04e-16 -6.76e-17 -2.14e-17 -3.63e-01  -1.59e-16
   dfb.e2.III dfb.e2.IV dfb.ep2.V dfb.e2.VI   dffit  cov.r   cook.d   hat inf
1    1.42e-01  1.42e-01  1.42e-01  1.42e-01  0.3474 2.6007 6.89e-03 0.375    
2   -8.64e-18 -2.95e-17 -2.63e-17 -1.43e-17  0.0630 2.9333 2.28e-04 0.375   *
3    1.29e-01 -2.20e-16 -2.13e-16 -1.90e-16 -0.3157 2.6576 5.69e-03 0.375    
4    2.12e-16 -1.42e-01  2.36e-16  1.61e-16  0.3474 2.6007 6.89e-03 0.375    
5   -3.03e-16 -2.04e-16  4.10e-01 -2.84e-16 -1.0036 1.0696 5.47e-02 0.375    
6    4.35e-16  3.81e-16  2.75e-16 -2.20e-01  0.5396 2.1848 1.65e-02 0.375    
7    1.87e-01  1.87e-01  1.87e-01  1.87e-01 -0.4592 2.3713 1.20e-02 0.375    
8    3.13e-17  1.27e-16  9.76e-17  5.10e-17  0.2998 2.6845 5.14e-03 0.375    
9   -1.48e-01 -5.74e-17 -1.02e-16 -1.36e-16 -0.3634 2.5707 7.53e-03 0.375    
10  -2.15e-17  1.22e-01 -2.71e-18  3.40e-18  0.2998 2.6845 5.14e-03 0.375    
11   7.51e-17  7.69e-17 -7.07e-02  6.48e-17 -0.1733 2.8554 1.72e-03 0.375   *
12  -8.13e-17 -1.19e-16 -9.31e-17  1.61e-01  0.3952 2.5077 8.90e-03 0.375    
13  -1.42e-01 -1.42e-01 -1.42e-01 -1.42e-01 -0.3474 2.6007 6.89e-03 0.375    
14  -3.57e-17 -6.78e-17 -6.59e-17 -9.72e-17 -0.2523 2.7580 3.64e-03 0.375    
15  -5.39e-01  7.65e-17 -5.48e-18  1.50e-17  1.3207 0.5276 9.11e-02 0.375    
16   1.24e-16  1.42e-01  1.62e-16  1.54e-16 -0.3474 2.6007 6.89e-03 0.375    
17   2.07e-17  2.62e-17  6.43e-02  5.35e-18 -0.1575 2.8708 1.42e-03 0.375   *
18   6.39e-17  5.85e-17  6.18e-17  6.43e-02 -0.1575 2.8708 1.42e-03 0.375   *
19   1.35e-01  1.35e-01  1.35e-01  1.35e-01 -0.3316 2.6297 6.28e-03 0.375    
20  -4.49e-17  1.01e-16 -2.96e-17  3.26e-17 -0.7187 1.7397 2.88e-02 0.375    
21   5.79e-02  8.00e-18  1.36e-17  6.42e-18  0.1417 2.8848 1.15e-03 0.375   *
22  -9.01e-17 -2.93e-01 -5.29e-17  0.00e+00 -0.7187 1.7397 2.88e-02 0.375    
23  -6.91e-17 -3.16e-17 -1.74e-01 -4.84e-18 -0.4272 2.4411 1.04e-02 0.375    
24   3.83e-16  9.12e-17  2.74e-16  9.49e-01  2.3242 0.0227 2.37e-01 0.375   *
25  -9.01e-02 -9.01e-02 -9.01e-02 -9.01e-02 -0.2206 2.8009 2.79e-03 0.375   *
26  -1.45e-19 -7.05e-17 -1.19e-16 -2.55e-16 -0.9017 1.2945 4.46e-02 0.375    
27  -2.60e-01 -1.97e-16 -2.08e-16 -2.67e-16  0.6368 1.9455 2.28e-02 0.375    
28  -2.82e-18 -6.43e-02 -6.41e-20 -1.25e-17  0.1575 2.8708 1.42e-03 0.375   *
29  -4.86e-17 -4.50e-17 -1.42e-01 -7.48e-17  0.3474 2.6007 6.89e-03 0.375    
30   8.60e-18  6.89e-18  4.94e-18  1.29e-02 -0.0315 2.9423 5.69e-05 0.375   *
31  -3.34e-01 -3.34e-01 -3.34e-01 -3.34e-01  0.8180 1.4934 3.70e-02 0.375    
32   1.10e-16  2.24e-16  4.08e-17  1.15e-16 -1.1248 0.8327 6.78e-02 0.375    
33   7.35e-01  1.40e-16  7.96e-17  2.65e-16  1.7998 0.1363 1.57e-01 0.375    
34  -2.54e-18  1.93e-02  1.09e-18 -1.07e-18  0.0472 2.9386 1.28e-04 0.375   *
35  -6.63e-18 -9.61e-18 -1.93e-02 -6.96e-18 -0.0472 2.9386 1.28e-04 0.375   *
36  -3.21e-17  1.26e-16  5.69e-17 -5.92e-01 -1.4496 0.3783 1.08e-01 0.375    
37   9.01e-02  9.01e-02  9.01e-02  9.01e-02  0.2206 2.8009 2.79e-03 0.375   *
38   6.60e-17  1.86e-16  1.94e-16  3.01e-16  1.1073 0.8646 6.58e-02 0.375    
39   6.94e-01  3.81e-16  3.94e-16  6.55e-16 -1.6995 0.1856 1.42e-01 0.375    
40   2.82e-17  6.43e-02  2.23e-17  4.46e-17 -0.1575 2.8708 1.42e-03 0.375   *
41  -1.40e-16 -4.45e-17 -3.27e-01 -9.08e-17  0.8013 1.5341 3.56e-02 0.375    
42   1.29e-16  1.07e-16  1.09e-16  1.42e-01 -0.3474 2.6007 6.89e-03 0.375    
43   6.43e-03  6.43e-03  6.43e-03  6.43e-03 -0.0157 2.9446 1.42e-05 0.375   *
44  -1.27e-16 -1.01e-16 -9.86e-17 -1.81e-16  1.6016 0.2478 1.28e-01 0.375    
45  -6.23e-01 -2.70e-16 -2.03e-16 -1.21e-16 -1.5249 0.3080 1.18e-01 0.375    
46  -1.95e-17  1.48e-01 -2.54e-17 -3.29e-17  0.3634 2.5707 7.53e-03 0.375    
47   1.27e-16  1.33e-16  2.67e-01  8.14e-17  0.6531 1.9045 2.39e-02 0.375    
48  -2.49e-16 -2.79e-16 -1.71e-16 -4.45e-01 -1.0899 0.8972 6.39e-02 0.375    
influenceIndexPlot(modelo.dbca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dbca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1     -0.39954801      2.754849  0.1228
   2     -0.16985195      2.280358  0.7780
   3      0.24871877      1.434951  0.0620
   4     -0.01896932      1.892341  0.8208
   5     -0.19045840      2.120818  0.4600
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dbca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dbca
DW = 2.7548, p-value = 0.1302
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.dbca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dbca)
W = 0.97148, p-value = 0.2889
ad.test(rstudent(modelo.dbca))

    Anderson-Darling normality test

data:  rstudent(modelo.dbca)
A = 0.52147, p-value = 0.1758
lillie.test(rstudent(modelo.dbca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dbca)
D = 0.10849, p-value = 0.169
ks.test(rstudent(modelo.dbca), "pnorm",
        alternative = "two.sided")

    Exact one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dbca)
D = 0.096609, p-value = 0.7251
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dbca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dbca)
W = 0.089678, p-value = 0.1511
pearson.test(rstudent(modelo.dbca))

    Pearson chi-square normality test

data:  rstudent(modelo.dbca)
P = 9.5, p-value = 0.2187
sf.test(rstudent(modelo.dbca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dbca)
W = 0.96843, p-value = 0.19

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dbca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 0.3413064, Df = 1, p = 0.55908
bptest(modelo.dbca)

    studentized Breusch-Pagan test

data:  modelo.dbca
BP = 24.756, df = 17, p-value = 0.1003
bptest(modelo.dbca, studentize = F)

    Breusch-Pagan test

data:  modelo.dbca
BP = 28.444, df = 17, p-value = 0.04001
olsrr::ols_test_breusch_pagan(modelo.dbca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

              Data               
 --------------------------------
 Response : rdto 
 Variables: fitted values of rdto 

        Test Summary         
 ----------------------------
 DF            =    1 
 Chi2          =    0.3413064 
 Prob > Chi2   =    0.5590761 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dbca %>% gvlma()

Call:
lm(formula = rdto ~ epoca * linaje + bloque %in% epoca + bloque, 
    data = data_D)

Coefficients:
     (Intercept)            epoca2           linaje2           linaje3  
       1.108e+01         5.125e+00        -1.667e-01        -1.500e+00  
         linaje4          bloqueII         bloqueIII          bloqueIV  
      -3.667e+00         1.750e+00         7.500e-01         1.000e+00  
         bloqueV          bloqueVI    epoca2:linaje2    epoca2:linaje3  
       2.500e+00         2.500e+00        -1.167e+00        -3.833e+00  
  epoca2:linaje4   epoca2:bloqueII  epoca2:bloqueIII   epoca2:bloqueIV  
      -3.500e+00         1.250e+00         1.000e+00        -9.971e-16  
  epoca2:bloqueV   epoca2:bloqueVI  
       7.500e-01         3.250e+00  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                     Value p-value                   Decision
Global Stat        10.1485 0.03800 Assumptions NOT satisfied!
Skewness            0.8206 0.36500    Assumptions acceptable.
Kurtosis            0.1776 0.67347    Assumptions acceptable.
Link Function       3.7952 0.05140    Assumptions acceptable.
Heteroscedasticity  5.3551 0.02066 Assumptions NOT satisfied!

Análisis de varianza

\[Y_{ijk} = \mu + \tau_{i} + \text{Error}(\tau\text{Bloque})_{i(k)} + \beta_{j} + (\tau\beta)_{ij} + \gamma_{k} + \epsilon_{ijk}\] \[\hat{Y}_{ijk} = \mu + \tau_{i} + \text{Error}(\tau\text{Bloque})_{i(k)} + \beta_{j} + \gamma_{k}\]

Dónde:

\(Y_{ijk}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijk}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor epoca.

\(\text{Error}(\tau\text{Bloque})_{i(k)}\) = Efecto del i-ésimo nivel de epoca en el l-ésimo nivel de Bloque.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor tratamiento (linaje).

\((\tau\beta)_{ij}\) = Efecto de la interacción entre el i-ésimo nivel del factor época y el j-ésimo nivel del factor linaje.

\(\gamma_{k}\) = Efecto del k-ésimo nivel de Bloque.

\(\epsilon_{ijk}\) = Residuo observado del modelo.

Pruebas de hipótesis

Para el factor A (epoca):

\(H_0: \tau_{A1} = \tau_{A2} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (linaje):

\(H_0: \beta_{B1} = \beta_{B2} = \beta_{B3} = \beta_{B4} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dbca, test = "F")
Analysis of Variance Table

Response: rdto
             Df  Sum Sq Mean Sq F value    Pr(>F)    
epoca         1 196.021 196.021 30.1377 5.845e-06 ***
linaje        3 223.396  74.465 11.4489 3.591e-05 ***
bloque        5  87.687  17.537  2.6963    0.0397 *  
epoca:linaje  3  30.729  10.243  1.5748    0.2160    
epoca:bloque  5  14.354   2.871  0.4414    0.8160    
Residuals    30 195.125   6.504                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
GAD::estimates(modelo.dbca)
$tm
             epoca linaje bloque        n
epoca            0      4      6 2.666667
linaje           2      0      6 2.666667
bloque           2      4      1 2.666667
epoca:linaje     0      0      6 2.666667
epoca:bloque     0      4      1 2.666667
Res              1      1      1 1.000000

$mse
             Mean square estimates       
epoca        "Res + epoca:bloque + epoca"
linaje       "Res + linaje"              
bloque       "Res + bloque"              
epoca:linaje "Res + epoca:linaje"        
epoca:bloque "Res + epoca:bloque"        
Residual     "Res"                       

$f.versus
             F-ratio versus
epoca        "epoca:bloque"
linaje       "Residual"    
bloque       "Residual"    
epoca:linaje "Residual"    
epoca:bloque "Residual"    
GAD::gad(modelo.dbca)
Analysis of Variance Table

Response: rdto
             Df  Sum Sq Mean Sq F value    Pr(>F)    
epoca         1 196.021 196.021 68.2801 0.0004234 ***
linaje        3 223.396  74.465 11.4489 3.591e-05 ***
bloque        5  87.687  17.537  2.6963 0.0397006 *  
epoca:linaje  3  30.729  10.243  1.5748 0.2160030    
epoca:bloque  5  14.354   2.871  0.4414 0.8159985    
Residual     30 195.125   6.504                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(epoca/Bloque)” en el caso de efectos aleatorios o “Error(epoca:Bloque)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos.

aov(rdto ~ bloque + epoca * linaje + Error(bloque %in% epoca) + bloque, data = data_D) -> aov.dbca
summary(aov.dbca)

Error: bloque:epoca
          Df Sum Sq Mean Sq F value   Pr(>F)    
bloque     5  87.69   17.54   6.109 0.034411 *  
epoca      1 196.02  196.02  68.280 0.000423 ***
Residuals  5  14.35    2.87                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Error: Within
             Df Sum Sq Mean Sq F value   Pr(>F)    
linaje        3 223.40   74.47  11.449 3.59e-05 ***
epoca:linaje  3  30.73   10.24   1.575    0.216    
Residuals    30 195.13    6.50                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
broom::tidy(aov.dbca)
# A tibble: 6 × 7
  stratum      term            df sumsq meansq statistic    p.value
  <chr>        <chr>        <dbl> <dbl>  <dbl>     <dbl>      <dbl>
1 bloque:epoca bloque           5  87.7  17.5       6.11  0.0344   
2 bloque:epoca epoca            1 196.  196.       68.3   0.000423 
3 bloque:epoca Residuals        5  14.4   2.87     NA    NA        
4 Within       linaje           3 223.   74.5      11.4   0.0000359
5 Within       epoca:linaje     3  30.7  10.2       1.57  0.216    
6 Within       Residuals       30 195.    6.50     NA    NA        
broom::tidy(gad(modelo.dbca))
# A tibble: 6 × 6
  term            df sumsq meansq statistic    p.value
  <chr>        <int> <dbl>  <dbl>     <dbl>      <dbl>
1 epoca            1 196.  196.      68.3    0.000423 
2 linaje           3 223.   74.5     11.4    0.0000359
3 bloque           5  87.7  17.5      2.70   0.0397   
4 epoca:linaje     3  30.7  10.2      1.57   0.216    
5 epoca:bloque     5  14.4   2.87     0.441  0.816    
6 Residual        30 195.    6.50    NA     NA        

Valor de la tabla de F para el factor lugar con una significancia de 0.05.

qf(0.95, 1, 5)
[1] 6.607891

Valor de la tabla de F para el factor linaje con una significancia de 0.05.

qf(0.95, 3, 30)
[1] 2.922277

Conclusión.

Con respecto al Factor epoca: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor epoca tienen un efecto sobre el rendimiento estadísticamente diferente a 0.

Con respecto al Factor linaje: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor linaje tienen un efecto sobre el rendimiento estadísticamente diferente a 0.

agricolae::cv.model(modelo.dbca)
[1] 19.33897

Comparaciones de medias para los efectos principales del Factor Lugar

get_df_ea(aov.dbca)
[1] 5
get_mse_ea(aov.dbca)
[1] 2.870833
data_D %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  epoca, # Cambiar según nombre de variable independiente
  DFerror = get_df_ea(aov.dbca), 
  MSerror = get_mse_ea(aov.dbca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ epoca

LSD t Test for rdto 

Mean Square Error:  2.870833 

epoca,  means and individual ( 95 %) CI

      rdto      std  r      LCL      UCL Min Max
1 11.16667 2.443566 24 10.27761 12.05572   4  15
2 15.20833 4.242427 24 14.31928 16.09739   7  26

Alpha: 0.05 ; DF Error: 5
Critical Value of t: 2.570582 

least Significant Difference: 1.257317 

Treatments with the same letter are not significantly different.

      rdto groups
2 15.20833      a
1 11.16667      b

Comparaciones de medias para los efectos principales del Factor Linaje

data_D %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  linaje, # Cambiar según nombre de variable independiente
  DFerror = df.residual(modelo.dbca), 
  MSerror = dvmisc::get_mse(modelo.dbca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ linaje

LSD t Test for rdto 

Mean Square Error:  6.504167 

linaje,  means and individual ( 95 %) CI

      rdto      std  r       LCL      UCL Min Max
1 15.58333 3.848455 12 14.079780 17.08689  11  23
2 14.83333 4.152400 12 13.329780 16.33689  10  26
3 12.16667 2.167249 12 10.663113 13.67022   9  17
4 10.16667 3.298301 12  8.663113 11.67022   4  16

Alpha: 0.05 ; DF Error: 30
Critical Value of t: 2.042272 

least Significant Difference: 2.126346 

Treatments with the same letter are not significantly different.

      rdto groups
1 15.58333      a
2 14.83333      a
3 12.16667      b
4 10.16667      b

Análisis de DBCA de dos vías con análisis completo


Importación de datos


data_D <- data %>%
  dplyr::filter(lugar %in% "Lima")

Definición del modelo


modelo.dbca <- lm(rdto ~ epoca * linaje + bloque %in% epoca + bloque, data = data_D)
summary(modelo.dbca)

Call:
lm(formula = rdto ~ epoca * linaje + bloque %in% epoca + bloque, 
    data = data_D)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.1667 -0.9271 -0.1042  0.9271  5.3750 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)       1.108e+01  1.562e+00   7.097 6.83e-08 ***
epoca2            5.125e+00  2.209e+00   2.320   0.0273 *  
linaje2          -1.667e-01  1.472e+00  -0.113   0.9106    
linaje3          -1.500e+00  1.472e+00  -1.019   0.3165    
linaje4          -3.667e+00  1.472e+00  -2.490   0.0185 *  
bloqueII          1.750e+00  1.803e+00   0.970   0.3396    
bloqueIII         7.500e-01  1.803e+00   0.416   0.6804    
bloqueIV          1.000e+00  1.803e+00   0.555   0.5833    
bloqueV           2.500e+00  1.803e+00   1.386   0.1759    
bloqueVI          2.500e+00  1.803e+00   1.386   0.1759    
epoca2:linaje2   -1.167e+00  2.082e+00  -0.560   0.5795    
epoca2:linaje3   -3.833e+00  2.082e+00  -1.841   0.0755 .  
epoca2:linaje4   -3.500e+00  2.082e+00  -1.681   0.1032    
epoca2:bloqueII   1.250e+00  2.550e+00   0.490   0.6276    
epoca2:bloqueIII  1.000e+00  2.550e+00   0.392   0.6978    
epoca2:bloqueIV  -9.971e-16  2.550e+00   0.000   1.0000    
epoca2:bloqueV    7.500e-01  2.550e+00   0.294   0.7707    
epoca2:bloqueVI   3.250e+00  2.550e+00   1.274   0.2123    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.55 on 30 degrees of freedom
Multiple R-squared:  0.7389,    Adjusted R-squared:  0.5909 
F-statistic: 4.994 on 17 and 30 DF,  p-value: 6.425e-05

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dbca)
ggResidpanel::resid_panel(modelo.dbca)
influence.measures(modelo.dbca)
Influence measures of
     lm(formula = rdto ~ epoca * linaje + bloque %in% epoca + bloque,      data = data_D) :

      dfb.1_ dfb.epc2  dfb.lnj2  dfb.lnj3  dfb.lnj4  dfb.blII  dfb.bIII
1   3.47e-01 -0.24568 -1.64e-01 -1.64e-01 -1.64e-01 -2.01e-01 -2.01e-01
2   2.10e-02 -0.01484 -2.97e-02 -2.97e-02 -2.97e-02  3.64e-02 -1.04e-17
3  -1.05e-01  0.07440  1.49e-01  1.49e-01  1.49e-01  2.59e-16 -1.82e-01
4   1.16e-01 -0.08189 -1.64e-01 -1.64e-01 -1.64e-01 -2.80e-16 -2.38e-16
5  -3.35e-01  0.23656  4.73e-01  4.73e-01  4.73e-01  1.63e-16  1.85e-16
6   1.80e-01 -0.12718 -2.54e-01 -2.54e-01 -2.54e-01 -1.57e-16 -4.67e-16
7   5.10e-16 -0.32469 -1.44e-16 -1.80e-16 -2.53e-16  4.98e-17 -7.58e-17
8   8.33e-17  0.07066 -6.57e-17 -6.63e-17 -3.68e-17 -2.29e-16 -5.64e-17
9   0.00e+00 -0.08564  2.30e-17  3.47e-18 -4.85e-17  1.96e-16  5.61e-19
10 -1.09e-16  0.07066  4.20e-17  3.78e-17  8.81e-17 -8.24e-17  3.92e-17
11  1.26e-16 -0.04084 -1.43e-17 -3.83e-17 -4.54e-17 -2.41e-18 -7.67e-17
12 -2.45e-16  0.09316  7.26e-17  8.91e-17  1.29e-16 -5.46e-17  9.94e-17
13 -1.93e-01  0.13649 -1.64e-01  2.67e-16  3.61e-16  2.01e-01  2.01e-01
14  2.80e-02 -0.01982 -1.19e-01 -1.03e-17 -3.73e-17 -1.46e-01  5.17e-18
15 -1.47e-01  0.10376  6.23e-01  7.58e-16  6.51e-16  0.00e+00  7.63e-01
16  3.86e-02 -0.02730 -1.64e-01  2.30e-17 -3.76e-17 -1.76e-17 -8.80e-17
17  1.75e-02 -0.01237 -7.42e-02 -2.19e-17 -2.40e-17  3.11e-18 -3.99e-18
18  1.75e-02 -0.01237 -7.42e-02 -2.01e-17 -3.03e-17  9.47e-18 -4.49e-17
19  1.98e-16 -0.13025 -1.62e-16 -9.90e-17 -9.97e-17 -1.29e-16 -3.39e-17
20  3.07e-17  0.05646 -2.28e-16 -2.29e-17 -4.06e-17 -8.22e-17  9.50e-17
21  4.54e-18 -0.01114  2.41e-17 -6.50e-18 -1.02e-17  3.10e-17  6.96e-19
22 -9.21e-17  0.05646 -1.59e-16 -9.07e-18 -1.72e-17 -9.60e-17  1.94e-16
23 -6.39e-17  0.03356 -8.65e-17  3.98e-17  3.61e-17 -4.41e-17  1.01e-16
24  3.48e-16 -0.18260  5.07e-16  9.79e-17 -3.80e-17  2.74e-16 -7.10e-16
25 -1.23e-01  0.08668  1.96e-16 -1.04e-01  2.56e-16  1.27e-01  1.27e-01
26  1.00e-01 -0.07085  2.36e-16 -4.25e-01  2.08e-17 -5.21e-01 -6.35e-17
27 -7.08e-02  0.05003  3.33e-16  3.00e-01  2.51e-16  1.90e-16  3.68e-01
28 -1.75e-02  0.01237 -8.24e-18  7.42e-02 -2.30e-18  2.39e-18  1.20e-17
29 -3.86e-02  0.02730  2.73e-17  1.64e-01  4.76e-18  5.11e-17  3.78e-17
30  3.50e-03 -0.00247 -4.12e-18 -1.48e-02 -2.20e-18  1.88e-18 -6.64e-18
31 -4.89e-16  0.32132  1.50e-16  2.24e-16  1.30e-16  2.75e-16  3.01e-16
32 -3.60e-17  0.08837 -3.71e-17 -9.70e-17  1.18e-16  1.75e-16 -8.25e-17
33  1.54e-16 -0.14141 -8.31e-17 -6.36e-17 -3.27e-16  2.71e-16  2.32e-16
34  3.03e-18 -0.00371 -4.52e-18 -2.41e-18 -7.44e-18  6.95e-18  1.25e-18
35 -1.16e-17  0.00371  2.11e-18  4.58e-18  9.16e-18  8.04e-19  4.96e-18
36 -1.55e-16  0.11389  1.16e-16  1.70e-17  2.75e-16 -1.86e-16  8.40e-17
37  1.23e-01 -0.08668 -1.41e-16 -1.29e-16  1.04e-01 -1.27e-01 -1.27e-01
38 -1.23e-01  0.08700 -5.44e-17  1.84e-16  5.22e-01  6.39e-01  8.17e-18
39  1.89e-01 -0.13352 -1.18e-15 -1.27e-15 -8.01e-01 -5.06e-16 -9.81e-01
40  1.75e-02 -0.01237 -2.09e-17 -1.31e-17 -7.42e-02 -2.59e-17 -3.19e-17
41 -8.90e-02  0.06296  1.93e-16  2.00e-16  3.78e-01  1.50e-16  3.99e-17
42  3.86e-02 -0.02730 -1.26e-16 -1.06e-16 -1.64e-01 -2.33e-17 -8.82e-17
43  8.07e-18 -0.00618 -3.11e-18 -3.95e-18 -3.53e-18 -2.71e-18 -5.49e-18
44 -5.13e-17 -0.12583 -5.13e-17 -5.13e-17 -1.03e-16  3.09e-17  1.95e-16
45 -3.10e-16  0.11981  2.31e-16  3.01e-16  3.91e-16  2.26e-17  9.49e-17
46  7.76e-18 -0.02855 -2.74e-17 -2.41e-17 -5.82e-17  2.58e-17  2.58e-17
47  1.40e-16 -0.05132 -4.57e-17 -6.28e-17 -1.26e-16 -8.67e-17 -6.24e-17
48 -2.45e-16  0.08563  7.82e-17  9.36e-18  1.40e-16  1.52e-16  1.74e-16
    dfb.blIV  dfb.blqV  dfb.blVI  dfb.e2.2  dfb.e2.3  dfb.e2.4 dfb.ep2.II
1  -2.01e-01 -2.01e-01 -2.01e-01  1.16e-01  1.16e-01  1.16e-01   1.42e-01
2   1.59e-17  6.23e-18 -8.66e-18  2.10e-02  2.10e-02  2.10e-02  -2.57e-02
3   2.24e-16  2.31e-16  2.01e-16 -1.05e-01 -1.05e-01 -1.05e-01  -1.72e-16
4   2.01e-01 -2.42e-16 -1.86e-16  1.16e-01  1.16e-01  1.16e-01   2.19e-16
5   1.31e-16 -5.79e-01  1.30e-16 -3.35e-01 -3.35e-01 -3.35e-01  -3.13e-16
6  -3.60e-16 -3.59e-16  3.12e-01  1.80e-01  1.80e-01  1.80e-01   6.67e-17
7  -1.23e-16 -1.74e-16 -1.39e-16  1.53e-01  1.53e-01  1.53e-01   1.87e-01
8  -1.45e-16 -1.46e-16 -7.89e-17 -9.99e-02 -9.99e-02 -9.99e-02   1.22e-01
9   5.33e-17  7.80e-17  1.35e-16  1.21e-01  1.21e-01  1.21e-01  -2.10e-16
10  2.26e-17  6.62e-18  1.60e-17 -9.99e-02 -9.99e-02 -9.99e-02   6.94e-17
11 -6.76e-17 -4.98e-17 -7.24e-17  5.78e-02  5.78e-02  5.78e-02   2.43e-17
12  1.01e-16  7.52e-17  1.54e-16 -1.32e-01 -1.32e-01 -1.32e-01   2.46e-17
13  2.01e-01  2.01e-01  2.01e-01  1.16e-01 -2.51e-16 -3.08e-16  -1.42e-01
14  4.18e-17  4.12e-17  6.77e-17  8.41e-02 -5.05e-17 -1.43e-17   1.03e-01
15 -1.92e-17  2.92e-17  1.16e-16 -4.40e-01 -5.40e-16 -5.09e-16  -9.27e-17
16 -2.01e-01 -1.48e-16 -1.50e-16  1.16e-01  8.30e-17  9.45e-17   5.54e-17
17  0.00e+00 -9.09e-02 -5.68e-18  5.25e-02  1.37e-17  5.80e-18   1.49e-17
18 -4.88e-17 -3.50e-17 -9.09e-02  5.25e-02  1.98e-17  3.03e-17   6.44e-18
19 -5.11e-17 -5.06e-17 -4.52e-17 -1.11e-01  6.09e-17  8.92e-17   1.35e-01
20 -1.28e-16 -2.57e-17 -5.47e-17 -2.40e-01  2.40e-17  6.92e-17  -2.93e-01
21  4.04e-18 -1.01e-18  4.54e-18  4.72e-02  8.00e-18  1.04e-17  -4.98e-18
22  9.91e-17  6.42e-17  4.03e-17 -2.40e-01  1.89e-17  4.48e-17   9.55e-17
23  1.60e-17  3.54e-17  1.54e-17 -1.42e-01 -5.92e-17 -4.72e-17   2.48e-17
24 -2.09e-16 -3.27e-16 -2.23e-16  7.75e-01 -1.06e-16  3.95e-17  -3.40e-16
25  1.27e-01  1.27e-01  1.27e-01 -1.84e-16  7.35e-02 -2.21e-16  -9.01e-02
26  3.48e-17  9.90e-17  2.25e-16 -4.34e-16  3.01e-01 -2.15e-16   3.68e-01
27  1.59e-16  1.44e-16  2.47e-16 -3.65e-16 -2.12e-01 -1.95e-16  -2.68e-16
28  9.09e-02  1.85e-17  3.45e-17 -2.33e-17 -5.25e-02 -2.50e-17   4.97e-18
29  4.55e-17  2.01e-01  6.91e-17 -1.93e-17 -1.16e-01  3.44e-17  -6.14e-17
30 -7.41e-18  0.00e+00 -1.82e-02  4.08e-18  1.05e-02  2.50e-18   1.32e-18
31  1.25e-16  2.87e-16  1.55e-16 -1.06e-16  2.73e-01 -1.37e-16  -3.34e-01
32 -1.55e-16 -5.95e-17 -8.26e-17  1.25e-16 -3.75e-01 -3.82e-17  -4.59e-01
33 -6.13e-17  4.59e-17 -9.13e-17  0.00e+00  6.00e-01  2.35e-16   3.16e-17
34  4.14e-18 -5.58e-19  6.31e-19  3.49e-18  1.57e-02  4.55e-18  -6.31e-18
35  8.37e-18  1.11e-17  5.99e-18  0.00e+00 -1.57e-02 -7.89e-18  -3.25e-18
36  7.15e-18 -2.56e-18  6.19e-17 -8.05e-17 -4.83e-01 -2.38e-16   2.34e-16
37 -1.27e-01 -1.27e-01 -1.27e-01  1.49e-16  1.52e-16 -7.35e-02   9.01e-02
38 -1.92e-16 -1.75e-16 -2.94e-16  4.63e-16  2.83e-16 -3.69e-01  -4.52e-01
39 -2.22e-16 -2.31e-16 -5.49e-16  1.13e-15  7.34e-16  5.66e-01   8.35e-16
40 -9.09e-02 -3.28e-17 -5.72e-17  2.78e-17  3.09e-17  5.25e-02   2.78e-17
41 -8.39e-17  4.63e-01  6.96e-17 -8.46e-17 -3.15e-17 -2.67e-01  -2.20e-16
42 -5.19e-17 -1.93e-17 -2.01e-01  1.13e-16  6.82e-17  1.16e-01   8.12e-17
43 -1.20e-18 -5.57e-18 -3.24e-18  2.47e-18  2.16e-18 -5.25e-03   6.43e-03
44  1.82e-16  1.93e-16  1.82e-16 -4.88e-17  3.14e-17  5.34e-01   6.54e-01
45  1.66e-16  1.08e-16  2.85e-17 -2.33e-16 -3.59e-16 -5.08e-01  -1.61e-16
46  5.55e-17  2.54e-17  2.23e-17  2.06e-17  2.14e-17  1.21e-01  -3.58e-17
47 -9.87e-17 -7.85e-17 -7.24e-17  4.20e-17  8.97e-17  2.18e-01   9.78e-17
48  2.39e-16  1.42e-16  2.04e-16 -6.76e-17 -2.14e-17 -3.63e-01  -1.59e-16
   dfb.e2.III dfb.e2.IV dfb.ep2.V dfb.e2.VI   dffit  cov.r   cook.d   hat inf
1    1.42e-01  1.42e-01  1.42e-01  1.42e-01  0.3474 2.6007 6.89e-03 0.375    
2   -8.64e-18 -2.95e-17 -2.63e-17 -1.43e-17  0.0630 2.9333 2.28e-04 0.375   *
3    1.29e-01 -2.20e-16 -2.13e-16 -1.90e-16 -0.3157 2.6576 5.69e-03 0.375    
4    2.12e-16 -1.42e-01  2.36e-16  1.61e-16  0.3474 2.6007 6.89e-03 0.375    
5   -3.03e-16 -2.04e-16  4.10e-01 -2.84e-16 -1.0036 1.0696 5.47e-02 0.375    
6    4.35e-16  3.81e-16  2.75e-16 -2.20e-01  0.5396 2.1848 1.65e-02 0.375    
7    1.87e-01  1.87e-01  1.87e-01  1.87e-01 -0.4592 2.3713 1.20e-02 0.375    
8    3.13e-17  1.27e-16  9.76e-17  5.10e-17  0.2998 2.6845 5.14e-03 0.375    
9   -1.48e-01 -5.74e-17 -1.02e-16 -1.36e-16 -0.3634 2.5707 7.53e-03 0.375    
10  -2.15e-17  1.22e-01 -2.71e-18  3.40e-18  0.2998 2.6845 5.14e-03 0.375    
11   7.51e-17  7.69e-17 -7.07e-02  6.48e-17 -0.1733 2.8554 1.72e-03 0.375   *
12  -8.13e-17 -1.19e-16 -9.31e-17  1.61e-01  0.3952 2.5077 8.90e-03 0.375    
13  -1.42e-01 -1.42e-01 -1.42e-01 -1.42e-01 -0.3474 2.6007 6.89e-03 0.375    
14  -3.57e-17 -6.78e-17 -6.59e-17 -9.72e-17 -0.2523 2.7580 3.64e-03 0.375    
15  -5.39e-01  7.65e-17 -5.48e-18  1.50e-17  1.3207 0.5276 9.11e-02 0.375    
16   1.24e-16  1.42e-01  1.62e-16  1.54e-16 -0.3474 2.6007 6.89e-03 0.375    
17   2.07e-17  2.62e-17  6.43e-02  5.35e-18 -0.1575 2.8708 1.42e-03 0.375   *
18   6.39e-17  5.85e-17  6.18e-17  6.43e-02 -0.1575 2.8708 1.42e-03 0.375   *
19   1.35e-01  1.35e-01  1.35e-01  1.35e-01 -0.3316 2.6297 6.28e-03 0.375    
20  -4.49e-17  1.01e-16 -2.96e-17  3.26e-17 -0.7187 1.7397 2.88e-02 0.375    
21   5.79e-02  8.00e-18  1.36e-17  6.42e-18  0.1417 2.8848 1.15e-03 0.375   *
22  -9.01e-17 -2.93e-01 -5.29e-17  0.00e+00 -0.7187 1.7397 2.88e-02 0.375    
23  -6.91e-17 -3.16e-17 -1.74e-01 -4.84e-18 -0.4272 2.4411 1.04e-02 0.375    
24   3.83e-16  9.12e-17  2.74e-16  9.49e-01  2.3242 0.0227 2.37e-01 0.375   *
25  -9.01e-02 -9.01e-02 -9.01e-02 -9.01e-02 -0.2206 2.8009 2.79e-03 0.375   *
26  -1.45e-19 -7.05e-17 -1.19e-16 -2.55e-16 -0.9017 1.2945 4.46e-02 0.375    
27  -2.60e-01 -1.97e-16 -2.08e-16 -2.67e-16  0.6368 1.9455 2.28e-02 0.375    
28  -2.82e-18 -6.43e-02 -6.41e-20 -1.25e-17  0.1575 2.8708 1.42e-03 0.375   *
29  -4.86e-17 -4.50e-17 -1.42e-01 -7.48e-17  0.3474 2.6007 6.89e-03 0.375    
30   8.60e-18  6.89e-18  4.94e-18  1.29e-02 -0.0315 2.9423 5.69e-05 0.375   *
31  -3.34e-01 -3.34e-01 -3.34e-01 -3.34e-01  0.8180 1.4934 3.70e-02 0.375    
32   1.10e-16  2.24e-16  4.08e-17  1.15e-16 -1.1248 0.8327 6.78e-02 0.375    
33   7.35e-01  1.40e-16  7.96e-17  2.65e-16  1.7998 0.1363 1.57e-01 0.375    
34  -2.54e-18  1.93e-02  1.09e-18 -1.07e-18  0.0472 2.9386 1.28e-04 0.375   *
35  -6.63e-18 -9.61e-18 -1.93e-02 -6.96e-18 -0.0472 2.9386 1.28e-04 0.375   *
36  -3.21e-17  1.26e-16  5.69e-17 -5.92e-01 -1.4496 0.3783 1.08e-01 0.375    
37   9.01e-02  9.01e-02  9.01e-02  9.01e-02  0.2206 2.8009 2.79e-03 0.375   *
38   6.60e-17  1.86e-16  1.94e-16  3.01e-16  1.1073 0.8646 6.58e-02 0.375    
39   6.94e-01  3.81e-16  3.94e-16  6.55e-16 -1.6995 0.1856 1.42e-01 0.375    
40   2.82e-17  6.43e-02  2.23e-17  4.46e-17 -0.1575 2.8708 1.42e-03 0.375   *
41  -1.40e-16 -4.45e-17 -3.27e-01 -9.08e-17  0.8013 1.5341 3.56e-02 0.375    
42   1.29e-16  1.07e-16  1.09e-16  1.42e-01 -0.3474 2.6007 6.89e-03 0.375    
43   6.43e-03  6.43e-03  6.43e-03  6.43e-03 -0.0157 2.9446 1.42e-05 0.375   *
44  -1.27e-16 -1.01e-16 -9.86e-17 -1.81e-16  1.6016 0.2478 1.28e-01 0.375    
45  -6.23e-01 -2.70e-16 -2.03e-16 -1.21e-16 -1.5249 0.3080 1.18e-01 0.375    
46  -1.95e-17  1.48e-01 -2.54e-17 -3.29e-17  0.3634 2.5707 7.53e-03 0.375    
47   1.27e-16  1.33e-16  2.67e-01  8.14e-17  0.6531 1.9045 2.39e-02 0.375    
48  -2.49e-16 -2.79e-16 -1.71e-16 -4.45e-01 -1.0899 0.8972 6.39e-02 0.375    
influenceIndexPlot(modelo.dbca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dbca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1     -0.39954801      2.754849  0.1340
   2     -0.16985195      2.280358  0.7880
   3      0.24871877      1.434951  0.0536
   4     -0.01896932      1.892341  0.8288
   5     -0.19045840      2.120818  0.4524
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dbca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dbca
DW = 2.7548, p-value = 0.1302
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.dbca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dbca)
W = 0.97148, p-value = 0.2889
ad.test(rstudent(modelo.dbca))

    Anderson-Darling normality test

data:  rstudent(modelo.dbca)
A = 0.52147, p-value = 0.1758
lillie.test(rstudent(modelo.dbca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dbca)
D = 0.10849, p-value = 0.169
ks.test(rstudent(modelo.dbca), "pnorm",
        alternative = "two.sided")

    Exact one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dbca)
D = 0.096609, p-value = 0.7251
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dbca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dbca)
W = 0.089678, p-value = 0.1511
pearson.test(rstudent(modelo.dbca))

    Pearson chi-square normality test

data:  rstudent(modelo.dbca)
P = 9.5, p-value = 0.2187
sf.test(rstudent(modelo.dbca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dbca)
W = 0.96843, p-value = 0.19

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dbca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 0.3413064, Df = 1, p = 0.55908
bptest(modelo.dbca)

    studentized Breusch-Pagan test

data:  modelo.dbca
BP = 24.756, df = 17, p-value = 0.1003
bptest(modelo.dbca, studentize = F)

    Breusch-Pagan test

data:  modelo.dbca
BP = 28.444, df = 17, p-value = 0.04001
olsrr::ols_test_breusch_pagan(modelo.dbca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

              Data               
 --------------------------------
 Response : rdto 
 Variables: fitted values of rdto 

        Test Summary         
 ----------------------------
 DF            =    1 
 Chi2          =    0.3413064 
 Prob > Chi2   =    0.5590761 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dbca %>% gvlma()

Call:
lm(formula = rdto ~ epoca * linaje + bloque %in% epoca + bloque, 
    data = data_D)

Coefficients:
     (Intercept)            epoca2           linaje2           linaje3  
       1.108e+01         5.125e+00        -1.667e-01        -1.500e+00  
         linaje4          bloqueII         bloqueIII          bloqueIV  
      -3.667e+00         1.750e+00         7.500e-01         1.000e+00  
         bloqueV          bloqueVI    epoca2:linaje2    epoca2:linaje3  
       2.500e+00         2.500e+00        -1.167e+00        -3.833e+00  
  epoca2:linaje4   epoca2:bloqueII  epoca2:bloqueIII   epoca2:bloqueIV  
      -3.500e+00         1.250e+00         1.000e+00        -9.971e-16  
  epoca2:bloqueV   epoca2:bloqueVI  
       7.500e-01         3.250e+00  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                     Value p-value                   Decision
Global Stat        10.1485 0.03800 Assumptions NOT satisfied!
Skewness            0.8206 0.36500    Assumptions acceptable.
Kurtosis            0.1776 0.67347    Assumptions acceptable.
Link Function       3.7952 0.05140    Assumptions acceptable.
Heteroscedasticity  5.3551 0.02066 Assumptions NOT satisfied!

Análisis de varianza

\[Y_{ijk} = \mu + \tau_{i} + \text{Error}(\tau\text{Bloque})_{i(k)} + \beta_{j} + (\tau\beta)_{ij} + \gamma_{k} + \epsilon_{ijk}\] \[\hat{Y}_{ijk} = \mu + \tau_{i} + \text{Error}(\tau\text{Bloque})_{i(k)} + \beta_{j} + \gamma_{k}\]

Dónde:

\(Y_{ijk}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijk}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor epoca.

\(\text{Error}(\tau\text{Bloque})_{i(k)}\) = Efecto del i-ésimo nivel de epoca en el k-ésimo nivel de Bloque.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor tratamiento (linaje).

\((\tau\beta)_{ij}\) = Efecto de la interacción entre el i-ésimo nivel del factor época y el j-ésimo nivel del factor linaje.

\(\gamma_{k}\) = Efecto del k-ésimo nivel de Bloque.

\(\epsilon_{ijk}\) = Residuo observado del modelo.

Pruebas de hipótesis

Para el factor A (epoca):

\(H_0: \tau_{A1} = \tau_{A2} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (linaje):

\(H_0: \beta_{B1} = \beta_{B2} = \beta_{B3} = \beta_{B4} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dbca, test = "F")
Analysis of Variance Table

Response: rdto
             Df  Sum Sq Mean Sq F value    Pr(>F)    
epoca         1 196.021 196.021 30.1377 5.845e-06 ***
linaje        3 223.396  74.465 11.4489 3.591e-05 ***
bloque        5  87.687  17.537  2.6963    0.0397 *  
epoca:linaje  3  30.729  10.243  1.5748    0.2160    
epoca:bloque  5  14.354   2.871  0.4414    0.8160    
Residuals    30 195.125   6.504                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
GAD::estimates(modelo.dbca)
$tm
             epoca linaje bloque        n
epoca            0      4      6 2.666667
linaje           2      0      6 2.666667
bloque           2      4      1 2.666667
epoca:linaje     0      0      6 2.666667
epoca:bloque     0      4      1 2.666667
Res              1      1      1 1.000000

$mse
             Mean square estimates       
epoca        "Res + epoca:bloque + epoca"
linaje       "Res + linaje"              
bloque       "Res + bloque"              
epoca:linaje "Res + epoca:linaje"        
epoca:bloque "Res + epoca:bloque"        
Residual     "Res"                       

$f.versus
             F-ratio versus
epoca        "epoca:bloque"
linaje       "Residual"    
bloque       "Residual"    
epoca:linaje "Residual"    
epoca:bloque "Residual"    
GAD::gad(modelo.dbca)
Analysis of Variance Table

Response: rdto
             Df  Sum Sq Mean Sq F value    Pr(>F)    
epoca         1 196.021 196.021 68.2801 0.0004234 ***
linaje        3 223.396  74.465 11.4489 3.591e-05 ***
bloque        5  87.687  17.537  2.6963 0.0397006 *  
epoca:linaje  3  30.729  10.243  1.5748 0.2160030    
epoca:bloque  5  14.354   2.871  0.4414 0.8159985    
Residual     30 195.125   6.504                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(epoca/Bloque)” en el caso de efectos aleatorios o “Error(epoca:Bloque)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos.

aov(rdto ~ bloque + epoca * linaje + Error(bloque %in% epoca) + bloque, data = data_D) -> aov.dbca
summary(aov.dbca)

Error: bloque:epoca
          Df Sum Sq Mean Sq F value   Pr(>F)    
bloque     5  87.69   17.54   6.109 0.034411 *  
epoca      1 196.02  196.02  68.280 0.000423 ***
Residuals  5  14.35    2.87                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Error: Within
             Df Sum Sq Mean Sq F value   Pr(>F)    
linaje        3 223.40   74.47  11.449 3.59e-05 ***
epoca:linaje  3  30.73   10.24   1.575    0.216    
Residuals    30 195.13    6.50                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
broom::tidy(aov.dbca)
# A tibble: 6 × 7
  stratum      term            df sumsq meansq statistic    p.value
  <chr>        <chr>        <dbl> <dbl>  <dbl>     <dbl>      <dbl>
1 bloque:epoca bloque           5  87.7  17.5       6.11  0.0344   
2 bloque:epoca epoca            1 196.  196.       68.3   0.000423 
3 bloque:epoca Residuals        5  14.4   2.87     NA    NA        
4 Within       linaje           3 223.   74.5      11.4   0.0000359
5 Within       epoca:linaje     3  30.7  10.2       1.57  0.216    
6 Within       Residuals       30 195.    6.50     NA    NA        
broom::tidy(gad(modelo.dbca))
# A tibble: 6 × 6
  term            df sumsq meansq statistic    p.value
  <chr>        <int> <dbl>  <dbl>     <dbl>      <dbl>
1 epoca            1 196.  196.      68.3    0.000423 
2 linaje           3 223.   74.5     11.4    0.0000359
3 bloque           5  87.7  17.5      2.70   0.0397   
4 epoca:linaje     3  30.7  10.2      1.57   0.216    
5 epoca:bloque     5  14.4   2.87     0.441  0.816    
6 Residual        30 195.    6.50    NA     NA        

Valor de la tabla de F para el factor lugar con una significancia de 0.05.

qf(0.95, 1, 5)
[1] 6.607891

Valor de la tabla de F para el factor linaje con una significancia de 0.05.

qf(0.95, 3, 30)
[1] 2.922277

Conclusión.

Con respecto al Factor epoca: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor epoca tienen un efecto sobre el rendimiento estadísticamente diferente a 0.

Con respecto al Factor linaje: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor linaje tienen un efecto sobre el rendimiento estadísticamente diferente a 0.

agricolae::cv.model(modelo.dbca)
[1] 19.33897

Comparaciones de medias para los efectos principales del Factor Lugar

get_df_ea(aov.dbca)
[1] 5
get_mse_ea(aov.dbca)
[1] 2.870833
data_D %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  epoca, # Cambiar según nombre de variable independiente
  DFerror = get_df_ea(aov.dbca), 
  MSerror = get_mse_ea(aov.dbca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ epoca

LSD t Test for rdto 

Mean Square Error:  2.870833 

epoca,  means and individual ( 95 %) CI

      rdto      std  r      LCL      UCL Min Max
1 11.16667 2.443566 24 10.27761 12.05572   4  15
2 15.20833 4.242427 24 14.31928 16.09739   7  26

Alpha: 0.05 ; DF Error: 5
Critical Value of t: 2.570582 

least Significant Difference: 1.257317 

Treatments with the same letter are not significantly different.

      rdto groups
2 15.20833      a
1 11.16667      b

Comparaciones de medias para los efectos principales del Factor Linaje

data_D %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  linaje, # Cambiar según nombre de variable independiente
  DFerror = df.residual(modelo.dbca), 
  MSerror = dvmisc::get_mse(modelo.dbca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ linaje

LSD t Test for rdto 

Mean Square Error:  6.504167 

linaje,  means and individual ( 95 %) CI

      rdto      std  r       LCL      UCL Min Max
1 15.58333 3.848455 12 14.079780 17.08689  11  23
2 14.83333 4.152400 12 13.329780 16.33689  10  26
3 12.16667 2.167249 12 10.663113 13.67022   9  17
4 10.16667 3.298301 12  8.663113 11.67022   4  16

Alpha: 0.05 ; DF Error: 30
Critical Value of t: 2.042272 

least Significant Difference: 2.126346 

Treatments with the same letter are not significantly different.

      rdto groups
1 15.58333      a
2 14.83333      a
3 12.16667      b
4 10.16667      b

Análisis de DBCA de dos vías con análisis combinado en un sitio


Definición del modelo


modelo.dbca <- lm(rdto ~ epoca * linaje * lugar + bloque %in% lugar + linaje:bloque %in% epoca + bloque %in% lugar:epoca + bloque, data = data)
summary(modelo.dbca)

Call:
lm(formula = rdto ~ epoca * linaje * lugar + bloque %in% lugar + 
    linaje:bloque %in% epoca + bloque %in% lugar:epoca + bloque, 
    data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.3750 -0.7917  0.0000  0.7917  3.3750 

Coefficients: (5 not defined because of singularities)
                              Estimate Std. Error t value Pr(>|t|)    
(Intercept)                  9.542e+00  2.193e+00   4.350 0.000145 ***
epoca2                       3.417e+00  3.102e+00   1.102 0.279434    
linaje2                      2.833e+00  2.857e+00   0.992 0.329296    
linaje3                     -1.250e+00  2.857e+00  -0.437 0.664885    
linaje4                     -7.500e-01  2.857e+00  -0.262 0.794732    
lugarPisco                   1.917e+00  2.291e+00   0.837 0.409395    
bloqueII                     6.750e+00  2.957e+00   2.282 0.029727 *  
bloqueIII                    3.750e-01  2.957e+00   0.127 0.899946    
bloqueIV                     2.375e+00  2.957e+00   0.803 0.428259    
bloqueV                      4.125e+00  2.957e+00   1.395 0.173324    
bloqueVI                     4.625e+00  2.957e+00   1.564 0.128342    
epoca2:linaje2              -1.000e+00  4.041e+00  -0.247 0.806219    
epoca2:linaje3               3.083e+00  4.041e+00   0.763 0.451376    
epoca2:linaje4              -3.750e+00  4.041e+00  -0.928 0.360779    
epoca2:lugarPisco           -2.833e+00  3.240e+00  -0.875 0.388762    
linaje2:lugarPisco           2.333e+00  2.160e+00   1.080 0.288601    
linaje3:lugarPisco           2.500e+00  2.160e+00   1.158 0.256199    
linaje4:lugarPisco           3.500e+00  2.160e+00   1.621 0.115589    
lugarPisco:bloqueII          1.250e+00  2.645e+00   0.473 0.639954    
lugarPisco:bloqueIII        -1.000e+00  2.645e+00  -0.378 0.708063    
lugarPisco:bloqueIV          4.000e+00  2.645e+00   1.512 0.140957    
lugarPisco:bloqueV          -5.000e-01  2.645e+00  -0.189 0.851350    
lugarPisco:bloqueVI         -1.250e+00  2.645e+00  -0.473 0.639954    
epoca2:linaje2:lugarPisco   -4.815e-15  3.054e+00   0.000 1.000000    
epoca2:linaje3:lugarPisco    3.833e+00  3.054e+00   1.255 0.219167    
epoca2:linaje4:lugarPisco    3.500e+00  3.054e+00   1.146 0.260907    
epoca1:linaje1:bloqueII     -2.375e+00  4.182e+00  -0.568 0.574365    
epoca2:linaje1:bloqueII     -6.874e-15  3.741e+00   0.000 1.000000    
epoca1:linaje2:bloqueII     -9.375e+00  4.182e+00  -2.241 0.032544 *  
epoca2:linaje2:bloqueII     -4.000e+00  3.741e+00  -1.069 0.293482    
epoca1:linaje3:bloqueII     -5.375e+00  4.182e+00  -1.285 0.208582    
epoca2:linaje3:bloqueII     -1.100e+01  3.741e+00  -2.940 0.006257 ** 
epoca1:linaje4:bloqueII     -2.875e+00  4.182e+00  -0.687 0.497115    
epoca2:linaje4:bloqueII             NA         NA      NA       NA    
epoca1:linaje1:bloqueIII     6.250e-01  4.182e+00   0.149 0.882212    
epoca2:linaje1:bloqueIII     4.000e+00  3.741e+00   1.069 0.293482    
epoca1:linaje2:bloqueIII     1.250e-01  4.182e+00   0.030 0.976355    
epoca2:linaje2:bloqueIII     1.500e+00  3.741e+00   0.401 0.691283    
epoca1:linaje3:bloqueIII     2.625e+00  4.182e+00   0.628 0.535002    
epoca2:linaje3:bloqueIII     4.300e-16  3.741e+00   0.000 1.000000    
epoca1:linaje4:bloqueIII    -1.875e+00  4.182e+00  -0.448 0.657158    
epoca2:linaje4:bloqueIII            NA         NA      NA       NA    
epoca1:linaje1:bloqueIV      1.625e+00  4.182e+00   0.389 0.700370    
epoca2:linaje1:bloqueIV      4.000e+00  3.741e+00   1.069 0.293482    
epoca1:linaje2:bloqueIV     -3.750e-01  4.182e+00  -0.090 0.929153    
epoca2:linaje2:bloqueIV     -3.000e+00  3.741e+00  -0.802 0.428893    
epoca1:linaje3:bloqueIV     -8.750e-01  4.182e+00  -0.209 0.835701    
epoca2:linaje3:bloqueIV     -6.500e+00  3.741e+00  -1.738 0.092549 .  
epoca1:linaje4:bloqueIV     -5.875e+00  4.182e+00  -1.405 0.170389    
epoca2:linaje4:bloqueIV             NA         NA      NA       NA    
epoca1:linaje1:bloqueV      -1.875e+00  4.182e+00  -0.448 0.657158    
epoca2:linaje1:bloqueV       2.500e+00  3.741e+00   0.668 0.509061    
epoca1:linaje2:bloqueV      -5.375e+00  4.182e+00  -1.285 0.208582    
epoca2:linaje2:bloqueV      -1.500e+00  3.741e+00  -0.401 0.691283    
epoca1:linaje3:bloqueV       3.125e+00  4.182e+00   0.747 0.460780    
epoca2:linaje3:bloqueV      -4.500e+00  3.741e+00  -1.203 0.238417    
epoca1:linaje4:bloqueV      -2.375e+00  4.182e+00  -0.568 0.574365    
epoca2:linaje4:bloqueV              NA         NA      NA       NA    
epoca1:linaje1:bloqueVI      1.500e+00  4.182e+00   0.359 0.722376    
epoca2:linaje1:bloqueVI      5.500e+00  3.741e+00   1.470 0.151911    
epoca1:linaje2:bloqueVI     -3.500e+00  4.182e+00  -0.837 0.409307    
epoca2:linaje2:bloqueVI      4.000e+00  3.741e+00   1.069 0.293482    
epoca1:linaje3:bloqueVI     -1.500e+00  4.182e+00  -0.359 0.722376    
epoca2:linaje3:bloqueVI     -5.000e+00  3.741e+00  -1.337 0.191412    
epoca1:linaje4:bloqueVI     -5.000e+00  4.182e+00  -1.195 0.241270    
epoca2:linaje4:bloqueVI             NA         NA      NA       NA    
epoca2:lugarPisco:bloqueII   2.250e+00  3.741e+00   0.601 0.552054    
epoca2:lugarPisco:bloqueIII  4.250e+00  3.741e+00   1.136 0.264915    
epoca2:lugarPisco:bloqueIV   3.250e+00  3.741e+00   0.869 0.391870    
epoca2:lugarPisco:bloqueV    2.250e+00  3.741e+00   0.601 0.552054    
epoca2:lugarPisco:bloqueVI  -1.539e-14  3.741e+00   0.000 1.000000    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.645 on 30 degrees of freedom
Multiple R-squared:  0.9065,    Adjusted R-squared:  0.7038 
F-statistic: 4.472 on 65 and 30 DF,  p-value: 1.292e-05

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dbca)
ggResidpanel::resid_panel(modelo.dbca)
influence.measures(modelo.dbca)
Influence measures of
     lm(formula = rdto ~ epoca * linaje * lugar + bloque %in% lugar +      linaje:bloque %in% epoca + bloque %in% lugar:epoca + bloque,      data = data) :

      dfb.1_ dfb.epc2  dfb.lnj2  dfb.lnj3  dfb.lnj4  dfb.lgrP  dfb.blII
1   2.54e+00 -1.79918 -1.66e+00 -1.66e+00 -1.66e+00 -1.33e+00  3.06e-15
2  -8.27e-02  0.05849  8.47e-02  8.47e-02  8.47e-02  1.58e-01  2.34e-15
3   4.12e-02 -0.02910 -4.21e-02 -4.21e-02 -4.21e-02 -7.88e-02  2.99e-16
4  -4.87e-02  0.03442  4.98e-02  4.98e-02  4.98e-02  9.32e-02 -6.11e-16
5  -7.13e-02  0.05043  7.30e-02  7.30e-02  7.30e-02  1.37e-01  4.67e-16
6  -6.00e-02  0.04241  6.14e-02  6.14e-02  6.14e-02  1.15e-01 -2.71e-16
7   1.10e-15  1.47126 -1.59e-15 -4.58e-16 -5.89e-16 -4.99e-16 -2.81e-01
8   8.06e-17  0.01850 -8.28e-17 -3.92e-18 -6.62e-17 -3.98e-17  3.88e-02
9  -7.05e-17 -0.02115 -1.77e-18  4.50e-17  6.87e-17 -4.95e-17 -1.43e-16
10 -2.31e-16 -0.08570  2.65e-16 -1.35e-16  2.28e-16 -1.52e-16  4.84e-16
11 -6.65e-17 -0.03708  1.11e-16  3.62e-17  9.33e-17 -5.16e-17 -3.58e-17
12  2.37e-17 -0.00528 -3.29e-17 -3.36e-17 -1.02e-17 -7.84e-18  1.41e-17
13 -3.71e-01  0.26248 -1.60e+00  1.02e-15  7.78e-16  7.11e-01  9.67e-16
14 -7.00e-02  0.04949  2.15e-01  7.94e-16  3.88e-16  1.34e-01  3.05e-15
15 -6.58e-02  0.04653  2.02e-01  1.83e-17  8.58e-17  1.26e-01 -2.54e-16
16  1.11e-01 -0.07846 -3.41e-01  1.18e-15  3.62e-16 -2.12e-01  1.24e-15
17 -5.76e-02  0.04073  1.77e-01  1.02e-16 -2.11e-17  1.10e-01 -1.12e-17
18  1.50e-02 -0.01059 -4.60e-02 -9.21e-17 -1.25e-16 -2.87e-02  1.01e-16
19  5.17e-17 -0.08405  1.62e-16 -5.00e-17 -1.81e-16 -7.48e-18  1.06e-01
20  4.15e-17  0.03318 -1.23e-16 -6.27e-17  2.40e-17 -4.68e-17 -2.09e-01
21 -4.61e-17 -0.00705  1.16e-16  3.43e-17  7.78e-18  4.01e-17 -1.75e-16
22 -6.44e-18  0.00352 -1.14e-17 -2.14e-17  1.67e-18  4.89e-17 -3.07e-17
23 -8.48e-19  0.00882  2.29e-17  7.95e-17  2.51e-17 -6.56e-17  4.83e-17
24  3.16e-16 -0.05760 -5.58e-16 -4.88e-16 -3.31e-16  1.48e-16 -2.00e-16
25  1.06e-01 -0.07513 -2.87e-16  4.57e-01 -2.99e-16 -2.03e-01 -3.58e-16
26  2.00e-02 -0.01414 -6.51e-17 -6.14e-02 -1.77e-16 -3.83e-02 -6.36e-16
27 -2.12e-02  0.01503  8.71e-17  6.52e-02  7.63e-17  4.07e-02 -1.90e-16
28 -3.65e-02  0.02582 -2.20e-17  1.12e-01 -2.45e-16  6.99e-02 -5.60e-16
29  8.00e-02 -0.05657 -3.57e-16 -2.46e-01 -7.34e-18 -1.53e-01 -1.16e-15
30 -1.75e-02  0.01236  1.05e-17  5.37e-02  4.60e-17  3.35e-02 -2.14e-17
31 -8.96e-17 -0.19411  2.51e-16  2.41e-16 -5.91e-16  7.00e-16  2.44e-01
32 -7.09e-17 -0.00970  7.24e-17  7.10e-19  7.51e-17  5.42e-17  6.10e-02
33 -1.15e-17 -0.03977  2.55e-16 -1.07e-16  3.83e-17 -1.64e-16 -5.78e-16
34 -1.81e-16 -0.02857  1.72e-16 -1.55e-16 -5.23e-17  2.70e-16 -5.90e-18
35 -3.65e-17  0.00882  1.15e-17  4.56e-17  3.86e-17  6.64e-17  9.71e-17
36 -3.80e-16  0.03041  4.07e-16  5.85e-16  1.63e-16  2.65e-16 -8.77e-17
37 -1.19e-01  0.08405  4.86e-17  1.46e-16 -5.11e-01  2.28e-01  6.01e-16
38  2.00e-02 -0.01414 -8.41e-17 -7.16e-17 -6.14e-02 -3.83e-02 -7.26e-16
39  1.08e-01 -0.07613  6.08e-17 -4.40e-16 -3.31e-01 -2.06e-01 -5.54e-16
40 -8.59e-02  0.06073 -8.86e-17 -4.83e-16  2.64e-01  1.64e-01 -1.17e-15
41 -4.43e-02  0.03133 -1.15e-16 -1.70e-16  1.36e-01  8.48e-02 -1.43e-16
42 -1.75e-02  0.01236  4.51e-18  8.94e-17  5.37e-02  3.35e-02 -1.44e-16
43 -9.88e-16  0.05736  4.26e-16  4.74e-16  7.43e-16  6.34e-16 -3.61e-01
44  2.28e-16 -0.01681 -3.82e-17 -1.33e-16 -1.14e-17 -1.67e-16  5.29e-01
45 -5.74e-16  0.03977 -7.51e-16  1.08e-16  7.89e-17 -2.44e-17  1.00e-15
46 -8.47e-18 -0.00352 -3.01e-18  5.97e-17  2.13e-17  2.28e-17  3.02e-17
47  6.23e-16 -0.03041 -7.41e-16 -7.15e-16 -8.32e-16 -6.84e-16  1.59e-16
48 -7.33e-16  0.02310  5.83e-16  7.50e-16  6.44e-16  3.98e-16 -1.68e-16
49 -1.16e+00  0.81781  1.18e+00  1.18e+00  1.18e+00 -1.33e+00  2.75e-15
50 -8.27e-02  0.05849  8.47e-02  8.47e-02  8.47e-02  1.58e-01  2.48e-15
51  4.12e-02 -0.02910 -4.21e-02 -4.21e-02 -4.21e-02 -7.88e-02  2.79e-16
52 -4.87e-02  0.03442  4.98e-02  4.98e-02  4.98e-02  9.32e-02 -5.85e-16
53 -7.13e-02  0.05043  7.30e-02  7.30e-02  7.30e-02  1.37e-01  2.66e-16
54 -6.00e-02  0.04241  6.14e-02  6.14e-02  6.14e-02  1.15e-01 -2.80e-16
55 -2.61e-15 -0.66875  1.49e-15  1.43e-15  1.48e-15  1.85e-15 -2.81e-01
56  1.04e-16  0.01850 -9.21e-17 -6.15e-17 -4.30e-17 -5.35e-17  3.88e-02
57 -1.03e-16 -0.02115  1.45e-17  4.12e-17  1.07e-16  2.31e-17 -1.51e-16
58 -3.19e-16 -0.08570  5.57e-16  2.61e-16  3.59e-16 -6.79e-17  4.63e-16
59 -2.80e-16 -0.03708  2.21e-16  1.38e-16  1.45e-16  1.40e-16 -7.67e-17
60  5.42e-18 -0.00528 -2.29e-17 -9.93e-18  1.58e-18 -1.30e-17  1.23e-17
61 -3.71e-01  0.26248  1.14e+00  6.60e-17  3.05e-16  7.11e-01  1.54e-15
62 -7.00e-02  0.04949  2.15e-01  6.27e-16  3.15e-16  1.34e-01  2.40e-15
63 -6.58e-02  0.04653  2.02e-01  3.54e-16  2.10e-16  1.26e-01 -2.45e-16
64  1.11e-01 -0.07846 -3.41e-01  5.44e-16  3.04e-16 -2.12e-01  7.27e-16
65 -5.76e-02  0.04073  1.77e-01 -3.84e-16  1.41e-17  1.10e-01 -3.65e-16
66  1.50e-02 -0.01059 -4.60e-02  3.61e-17 -4.77e-17 -2.87e-02  1.21e-16
67  5.17e-16 -0.08405  6.78e-17 -1.97e-16 -2.48e-16 -3.94e-16  1.06e-01
68 -1.34e-16  0.03318 -5.16e-17 -1.18e-16  5.69e-17  3.26e-16 -2.09e-01
69 -6.10e-18 -0.00705  6.25e-17  2.17e-17  1.80e-17 -4.55e-17 -1.38e-16
70 -2.44e-17  0.00352  2.15e-17 -1.92e-17  4.41e-18  5.27e-17 -2.31e-17
71 -7.63e-18  0.00882  4.12e-17  5.24e-17  2.61e-17  2.20e-17  3.82e-17
72  4.49e-16 -0.05760 -5.30e-16 -6.32e-16 -4.57e-16  5.21e-17 -1.89e-16
73  1.06e-01 -0.07513  0.00e+00 -3.26e-01 -3.47e-16 -2.03e-01 -3.42e-16
74  2.00e-02 -0.01414 -2.19e-16 -6.14e-02 -2.66e-16 -3.83e-02 -5.66e-16
75 -2.12e-02  0.01503 -2.31e-17  6.52e-02  5.17e-17  4.07e-02 -2.27e-16
76 -3.65e-02  0.02582 -1.76e-17  1.12e-01 -1.82e-16  6.99e-02 -4.89e-16
77  8.00e-02 -0.05657 -2.31e-16 -2.46e-01  9.30e-17 -1.53e-01 -1.13e-15
78 -1.75e-02  0.01236 -4.85e-17  5.37e-02 -6.29e-18  3.35e-02 -6.03e-18
79  7.47e-16 -0.19411 -2.84e-16 -6.54e-16 -5.85e-16  6.37e-17  2.44e-01
80 -1.59e-17 -0.00970  7.39e-17  2.68e-17  3.61e-17  2.56e-17  6.10e-02
81  2.87e-16 -0.03977  1.21e-16 -3.46e-16 -2.96e-16 -1.42e-16 -5.86e-16
82 -2.75e-16 -0.02857  2.60e-16  1.13e-16  8.90e-18  2.54e-16  1.42e-16
83 -4.49e-17  0.00882  1.52e-17  5.54e-17  2.64e-17  4.37e-17  1.19e-16
84 -3.83e-16  0.03041  4.35e-16  4.13e-16  1.07e-16  2.49e-16 -8.78e-17
85 -1.19e-01  0.08405  2.04e-16  2.67e-16  3.65e-01  2.28e-01  2.86e-16
86  2.00e-02 -0.01414 -1.55e-16 -1.53e-16 -6.14e-02 -3.83e-02 -6.35e-16
87  1.08e-01 -0.07613 -1.80e-16 -3.85e-16 -3.31e-01 -2.06e-01  2.73e-16
88 -8.59e-02  0.06073  2.30e-18 -2.42e-16  2.64e-01  1.64e-01 -9.43e-16
89 -4.43e-02  0.03133  4.47e-17  1.02e-16  1.36e-01  8.48e-02 -4.02e-18
90 -1.75e-02  0.01236  5.09e-18  8.94e-18  5.37e-02  3.35e-02 -2.00e-16
91  5.65e-16  0.05736 -3.45e-16 -4.42e-16 -4.42e-16 -5.57e-16  2.17e-01
92 -3.62e-16 -0.01681  1.59e-16  1.39e-16  1.50e-16  2.82e-16 -3.17e-01
93  3.17e-16  0.03977  6.06e-16 -3.94e-16 -3.20e-16  4.88e-17 -5.48e-16
94 -4.37e-17 -0.00352  4.00e-17 -2.39e-17  2.87e-17  4.42e-17  1.20e-17
95 -8.01e-16 -0.03041  6.81e-16  5.96e-16  4.38e-16  4.86e-16  4.19e-16
96  3.80e-16  0.02310 -1.74e-16 -3.66e-16 -3.35e-16 -1.42e-16 -3.03e-16
    dfb.bIII  dfb.blIV  dfb.blqV  dfb.blVI dfb.ep2.2 dfb.ep2.3 dfb.ep2.4
1   1.64e-15  1.77e-15  2.72e-15  2.59e-15  1.17e+00  1.17e+00  1.17e+00
2   1.75e-15  1.67e-15  1.36e-15  1.60e-15 -5.99e-02 -5.99e-02 -5.99e-02
3   6.63e-16  1.40e-16  1.61e-16  1.63e-16  2.98e-02  2.98e-02  2.98e-02
4  -2.46e-16 -7.61e-16 -5.41e-16 -5.68e-16 -3.52e-02 -3.52e-02 -3.52e-02
5   6.34e-16  6.63e-16  1.16e-15  5.91e-16 -5.16e-02 -5.16e-02 -5.16e-02
6  -3.58e-17  1.56e-17 -1.61e-16  7.97e-17 -4.34e-02 -4.34e-02 -4.34e-02
7  -2.81e-01 -2.81e-01 -2.81e-01 -2.81e-01 -9.58e-01 -9.58e-01 -9.58e-01
8   3.29e-16  1.33e-16  1.48e-16  1.14e-16 -1.89e-02 -1.89e-02 -1.89e-02
9  -4.44e-02 -2.43e-16 -1.74e-16 -1.62e-16  2.16e-02  2.16e-02  2.16e-02
10  5.63e-16 -1.80e-01  7.77e-16  3.52e-16  8.77e-02  8.77e-02  8.77e-02
11  7.91e-20  9.97e-18 -7.78e-02 -1.63e-16  3.79e-02  3.79e-02  3.79e-02
12  1.58e-17  1.33e-17  1.43e-17 -1.11e-02  5.41e-03  5.41e-03  5.41e-03
13  4.77e-16  3.87e-16  2.60e-16  1.04e-16  1.13e+00 -6.05e-16 -8.90e-16
14  1.67e-15  1.76e-15  1.57e-15  1.39e-15 -1.52e-01 -1.29e-15 -1.86e-15
15 -9.85e-16 -1.42e-16 -1.57e-16 -3.06e-16 -1.43e-01 -4.82e-17 -1.92e-16
16  1.35e-16  1.66e-15  1.38e-15  1.31e-15  2.41e-01 -1.23e-15 -1.09e-15
17  4.68e-17  4.09e-16  3.19e-16  2.14e-16 -1.25e-01  2.95e-16  4.21e-16
18  9.60e-18  4.86e-17  3.31e-17  4.97e-17  3.25e-02 -2.80e-17 -2.15e-17
19  1.06e-01  1.06e-01  1.06e-01  1.06e-01 -3.61e-01  2.21e-16  3.66e-16
20  2.63e-16 -1.68e-16 -5.60e-17 -2.57e-16 -1.02e-01  1.54e-16  8.71e-17
21  4.44e-02 -1.70e-16 -1.42e-16 -1.46e-16  2.16e-02 -3.16e-17  9.08e-17
22 -1.86e-17 -2.22e-02 -5.62e-17 -4.49e-17 -1.08e-02 -3.85e-18 -2.71e-18
23 -4.33e-17 -3.56e-17 -5.55e-02  4.82e-18 -2.71e-02 -7.63e-17 -8.51e-18
24  1.68e-16 -3.05e-16 -1.48e-16  3.62e-01  1.77e-01  6.43e-16  5.35e-16
25 -3.53e-16 -2.03e-16 -2.40e-16 -2.70e-16  3.04e-16 -3.23e-01  4.05e-16
26 -3.83e-16 -2.82e-16 -1.18e-16 -2.12e-16  2.04e-16  4.34e-02  5.08e-16
27 -5.25e-16 -2.09e-16 -2.83e-16 -1.87e-16 -1.21e-16 -4.61e-02  4.27e-17
28 -1.46e-16 -6.98e-16 -5.99e-16 -5.78e-16  2.49e-16 -7.93e-02  7.14e-16
29 -1.43e-15 -1.37e-15 -2.37e-15 -1.14e-15  2.32e-16  1.74e-01  9.82e-16
30  8.81e-17  1.02e-16 -9.16e-18  2.02e-16  5.81e-17 -3.79e-02 -6.04e-18
31  2.44e-01  2.44e-01  2.44e-01  2.44e-01  2.25e-16 -8.34e-01  4.77e-16
32 -1.03e-16 -3.85e-17 -5.12e-17 -2.47e-17 -5.73e-17  2.98e-02 -1.39e-17
33  2.50e-01 -3.66e-16 -1.60e-16 -3.62e-16 -1.53e-16  1.22e-01 -3.34e-17
34  1.62e-16  1.80e-01  1.36e-16 -1.02e-16 -7.23e-17  8.77e-02  2.00e-18
35  1.10e-16  8.89e-17 -5.55e-02  8.30e-17  2.55e-17 -2.71e-02 -7.91e-17
36  8.92e-17 -1.33e-16 -1.04e-16 -1.91e-01 -4.40e-16 -9.34e-02 -1.66e-16
37  4.54e-16  3.02e-16  5.00e-17  2.80e-16 -6.68e-17 -1.03e-16  3.61e-01
38 -5.04e-16 -4.60e-16 -4.31e-16 -5.08e-16  1.73e-16  2.64e-16  4.34e-02
39 -1.45e-16 -4.19e-16 -8.07e-17 -3.29e-16  2.06e-16  3.89e-17  2.34e-01
40 -8.04e-16 -1.49e-15 -1.37e-15 -1.24e-15  1.12e-16  5.12e-16 -1.86e-01
41  1.79e-16 -5.19e-17  2.67e-16  4.11e-17  1.05e-16  2.80e-16 -9.62e-02
42 -7.62e-17 -2.67e-17 -5.24e-17 -9.87e-17  2.49e-17 -7.27e-17 -3.79e-02
43 -3.61e-01 -3.61e-01 -3.61e-01 -3.61e-01 -3.37e-16 -2.82e-16  2.47e-01
44 -5.22e-16 -3.19e-16 -2.05e-16 -2.57e-16 -6.26e-17  1.29e-17  5.16e-02
45 -1.25e+00  5.09e-16  1.93e-16  1.39e-16 -3.02e-16  1.42e-16 -1.22e-01
46 -1.10e-17  1.11e-01  8.42e-17  4.58e-17 -1.50e-17 -1.80e-18  1.08e-02
47  9.50e-17  0.00e+00  9.57e-01  7.01e-17  1.34e-16  3.58e-16  9.34e-02
48 -4.52e-16 -4.15e-16 -2.37e-16 -7.27e-01 -6.39e-16 -8.39e-16 -7.09e-02
49  1.69e-15  2.23e-15  2.88e-15  2.29e-15 -8.37e-01 -8.37e-01 -8.37e-01
50  1.77e-15  1.67e-15  1.35e-15  1.57e-15 -5.99e-02 -5.99e-02 -5.99e-02
51  5.70e-16  1.10e-16  1.45e-16  1.37e-16  2.98e-02  2.98e-02  2.98e-02
52 -2.77e-16 -6.57e-16 -5.67e-16 -5.37e-16 -3.52e-02 -3.52e-02 -3.52e-02
53  5.18e-16  5.76e-16  9.97e-16  4.58e-16 -5.16e-02 -5.16e-02 -5.16e-02
54  1.36e-17  1.83e-17 -8.30e-17  1.64e-16 -4.34e-02 -4.34e-02 -4.34e-02
55 -2.81e-01 -2.81e-01 -2.81e-01 -2.81e-01  6.84e-01  6.84e-01  6.84e-01
56  2.52e-16  4.41e-17  1.16e-16  9.14e-17 -1.89e-02 -1.89e-02 -1.89e-02
57 -4.44e-02 -2.52e-16 -2.25e-16 -1.71e-16  2.16e-02  2.16e-02  2.16e-02
58  6.19e-16 -1.80e-01  6.81e-16  4.13e-16  8.77e-02  8.77e-02  8.77e-02
59 -7.53e-17 -5.98e-17 -7.78e-02 -1.85e-16  3.79e-02  3.79e-02  3.79e-02
60  1.25e-17  1.01e-17  2.18e-17 -1.11e-02  5.41e-03  5.41e-03  5.41e-03
61  9.46e-16  7.53e-16  3.46e-16  5.45e-16 -8.06e-01 -2.72e-16 -5.12e-16
62  1.59e-15  1.56e-15  1.34e-15  1.32e-15 -1.52e-01 -1.18e-15 -1.77e-15
63 -6.83e-16 -1.85e-16 -1.35e-16 -9.47e-17 -1.43e-01 -3.89e-16 -1.84e-16
64 -3.81e-16  8.66e-16  1.10e-15  9.35e-16  2.41e-01 -1.00e-15 -9.25e-16
65 -7.73e-17  1.09e-16 -2.50e-16 -1.77e-17 -1.25e-01  3.46e-16  3.62e-16
66  3.96e-17  1.06e-16  5.89e-17  2.88e-17  3.25e-02 -8.60e-17 -4.12e-17
67  1.06e-01  1.06e-01  1.06e-01  1.06e-01  2.58e-01  1.09e-16  2.85e-16
68  7.60e-17 -2.91e-16 -1.50e-16 -4.02e-16 -1.02e-01  1.90e-16  7.48e-17
69  4.44e-02 -1.78e-16 -1.44e-16 -1.35e-16  2.16e-02 -4.53e-17  5.40e-17
70 -7.57e-18 -2.22e-02 -4.11e-17 -4.53e-17 -1.08e-02  1.25e-17  1.17e-17
71  6.94e-18  7.11e-18 -5.55e-02  7.74e-17 -2.71e-02 -2.48e-17  3.14e-17
72 -1.09e-16 -3.46e-16 -2.71e-16  3.62e-01  1.77e-01  4.78e-16  4.45e-16
73 -2.31e-16 -2.62e-16 -2.74e-16 -1.59e-16  1.01e-16  2.31e-01  4.07e-16
74 -3.93e-16 -3.58e-16 -1.73e-16 -2.07e-16  3.53e-16  4.34e-02  5.97e-16
75 -5.21e-16 -1.90e-16 -3.03e-16 -1.71e-16 -2.72e-17 -4.61e-02  9.00e-17
76 -1.60e-16 -5.62e-16 -5.93e-16 -5.51e-16  2.21e-16 -7.93e-02  6.98e-16
77 -1.45e-15 -1.41e-15 -2.43e-15 -1.08e-15 -1.36e-17  1.74e-01  8.42e-16
78  1.39e-16  1.07e-16  2.34e-17  2.14e-16  1.79e-16 -3.79e-02  4.83e-17
79  2.44e-01  2.44e-01  2.44e-01  2.44e-01  2.99e-16  5.96e-01  7.59e-16
80 -1.11e-16 -1.90e-17 -2.80e-17 -2.74e-17 -8.18e-17  2.98e-02 -2.61e-17
81  2.50e-01 -3.45e-16 -1.58e-16 -4.38e-16  4.79e-18  1.22e-01  2.20e-16
82  2.45e-16  1.80e-01  2.79e-16 -1.03e-16 -1.48e-16  8.77e-02 -1.16e-16
83  1.47e-16  1.21e-16 -5.55e-02  1.12e-16 -1.38e-17 -2.71e-02 -1.13e-16
84 -7.51e-17 -1.34e-16 -1.43e-16 -1.91e-01 -4.87e-16 -9.34e-02 -1.37e-16
85  1.38e-16  6.10e-17  2.46e-16  2.55e-16 -2.92e-16 -2.92e-16 -2.58e-01
86 -5.24e-16 -4.50e-16 -3.99e-16 -5.07e-16  2.85e-16  4.30e-16  4.34e-02
87  1.27e-15 -1.07e-16  7.68e-17 -1.20e-16  4.78e-16  1.95e-16  2.34e-01
88 -8.20e-16 -1.37e-15 -8.28e-16 -9.82e-16 -2.13e-16  1.09e-16 -1.86e-01
89  2.26e-16  8.76e-17  3.92e-16  1.83e-16 -5.38e-17 -4.81e-17 -9.62e-02
90 -1.30e-16 -9.37e-17 -1.29e-16 -2.09e-16  5.79e-17  4.42e-17 -3.79e-02
91  2.17e-01  2.17e-01  2.17e-01  2.17e-01  1.49e-16  2.82e-16 -1.76e-01
92 -4.55e-16 -1.98e-16 -3.05e-16 -3.55e-16  7.14e-17  9.89e-17  5.16e-02
93  7.51e-01  9.34e-17  1.46e-16  4.61e-17 -1.69e-16 -1.32e-16 -1.22e-01
94  3.30e-17 -6.65e-02  1.26e-17  2.19e-17 -2.19e-17 -1.98e-17  1.08e-02
95  4.06e-16  2.94e-16 -5.74e-01  8.99e-17 -3.97e-16 -2.33e-16  9.34e-02
96 -1.55e-16 -1.61e-16 -3.16e-16  4.36e-01 -9.54e-17  3.48e-16 -7.09e-02
   dfb.ep2.P  dfb.l2.P  dfb.l3.P  dfb.l4.P dfb.lgP.II dfb.lP.III dfb.lP.IV
1    0.93959  6.26e-01  6.26e-01  6.26e-01   7.67e-01   7.67e-01  7.67e-01
2   -0.11200 -2.24e-01 -2.24e-01 -2.24e-01   2.74e-01   2.36e-17  1.29e-16
3    0.05573  1.11e-01  1.11e-01  1.11e-01   1.99e-16  -1.37e-01  6.04e-17
4   -0.06590 -1.32e-01 -1.32e-01 -1.32e-01  -1.99e-16  -1.50e-17  1.61e-01
5   -0.09656 -1.93e-01 -1.93e-01 -1.93e-01  -4.49e-16  -1.82e-16 -2.27e-16
6   -0.08120 -1.62e-01 -1.62e-01 -1.62e-01   3.12e-16   5.07e-16  5.45e-16
7   -0.76834  1.85e-15  1.61e-15  1.65e-15  -2.07e-15  -6.16e-16  1.35e-17
8   -0.03543  3.22e-18  1.24e-17  3.07e-17  -3.38e-17   2.98e-17  8.88e-17
9    0.04050  8.35e-18  5.85e-17  4.28e-17  -1.33e-17  -6.38e-17  6.83e-18
10   0.16409  3.07e-16  4.24e-16  1.10e-16  -8.24e-17  -2.87e-16 -3.35e-16
11   0.07100 -4.85e-17 -1.12e-17 -3.41e-17   3.08e-17   2.24e-17  3.26e-17
12   0.01012  3.15e-18  2.08e-17  2.92e-18  -4.74e-18  -9.66e-18 -1.19e-17
13  -0.50260  6.03e-01 -1.13e-16 -1.24e-16  -7.39e-01  -7.39e-01 -7.39e-01
14  -0.09477 -5.69e-01 -8.67e-16 -6.28e-16  -6.96e-01   7.05e-16  6.40e-16
15  -0.08911 -5.35e-01  2.51e-16  1.96e-16  -7.57e-16  -6.55e-01 -5.98e-16
16   0.15023  9.01e-01 -1.30e-15 -2.20e-16   4.56e-16  -2.40e-16  1.10e+00
17  -0.07799 -4.68e-01 -9.91e-16 -6.00e-16  -4.85e-16   8.83e-17 -7.35e-17
18   0.02027  1.22e-01  5.75e-17  1.51e-16  -1.52e-16  -2.15e-16 -2.21e-16
19   0.16094 -1.32e-16 -8.13e-17 -1.33e-16   4.44e-17  -4.43e-19 -2.36e-17
20  -0.06354  2.31e-17 -1.58e-16 -1.32e-16   3.35e-16   2.15e-16  9.17e-17
21   0.01350 -9.85e-17 -6.82e-17 -7.47e-17   4.15e-17   7.11e-17 -5.05e-17
22  -0.00675 -1.92e-17 -8.32e-18 -1.52e-18  -4.46e-17  -2.88e-17 -2.83e-17
23  -0.01688  1.34e-17 -1.09e-17  2.72e-17   5.42e-17   5.26e-17  7.48e-17
24   0.11029  9.72e-17 -2.09e-16 -1.22e-16  -1.39e-16  -1.90e-16 -3.78e-16
25   0.14386  1.42e-16 -1.73e-01  3.02e-16   2.11e-01   2.11e-01  2.11e-01
26   0.02707  3.00e-16  1.62e-01  2.16e-16   1.99e-01  -7.78e-17 -1.13e-16
27  -0.02877 -5.42e-17 -1.73e-01  2.98e-17  -1.22e-16  -2.11e-01 -4.62e-17
28  -0.04945 -1.40e-16 -2.97e-01  2.69e-17   2.73e-17   1.92e-16 -3.63e-01
29   0.10832  9.69e-16  6.50e-01  5.82e-16   8.44e-16   4.23e-16  4.08e-16
30  -0.02367 -6.69e-17 -1.42e-01 -5.19e-17   1.34e-16   1.75e-16  3.13e-16
31   0.37170 -4.99e-16 -1.85e-16  6.74e-19  -1.15e-15  -3.52e-16 -4.63e-16
32   0.01858  7.35e-17  9.09e-17  7.05e-17  -2.25e-16  -1.14e-16 -1.27e-16
33   0.07616 -6.65e-17  4.70e-17 -5.83e-17   1.46e-16   3.61e-16  5.88e-17
34   0.05470 -9.05e-17  1.41e-16 -4.55e-17  -2.17e-16  -2.80e-16 -5.60e-16
35  -0.01688 -2.97e-17 -9.39e-17 -1.91e-17  -5.29e-17  -1.39e-17 -1.90e-17
36  -0.05822 -2.73e-16 -3.31e-16 -1.38e-16  -2.43e-16   1.09e-16 -1.06e-16
37  -0.16094 -9.59e-17 -1.29e-16  1.93e-01  -2.37e-01  -2.37e-01 -2.37e-01
38   0.02707  1.78e-16  1.89e-16  1.62e-01   1.99e-01  -2.50e-17  4.16e-17
39   0.14578 -3.96e-16 -3.64e-16  8.75e-01   9.77e-17   1.07e+00 -2.06e-16
40  -0.11628  4.05e-16  6.39e-16 -6.98e-01  -6.77e-16  -2.65e-16 -8.55e-01
41  -0.05999 -1.93e-16 -2.40e-16 -3.60e-01  -4.90e-16  -9.85e-17 -3.39e-16
42  -0.02367  3.64e-17  5.91e-17 -1.42e-01   7.67e-17   1.25e-16  1.55e-16
43  -0.10984 -8.86e-16 -1.07e-15 -8.62e-16   1.05e-15  -2.37e-16  3.73e-17
44   0.03219  5.73e-16  6.90e-16  5.76e-16  -1.12e-15  -2.26e-16 -2.66e-16
45  -0.07616  4.87e-16  6.47e-16  5.71e-16  -1.64e-16  -2.36e-15 -2.02e-16
46   0.00675 -8.65e-18 -3.36e-17 -2.33e-17  -3.27e-17  -5.05e-17  4.20e-17
47   0.05822  8.53e-16  1.18e-15  7.39e-16   3.02e-16  -2.38e-16  9.08e-17
48  -0.04423 -4.14e-16 -4.06e-16 -4.59e-16   6.93e-17   8.49e-17  1.06e-16
49   0.93959  6.26e-01  6.26e-01  6.26e-01   7.67e-01   7.67e-01  7.67e-01
50  -0.11200 -2.24e-01 -2.24e-01 -2.24e-01   2.74e-01   2.28e-16  1.96e-16
51   0.05573  1.11e-01  1.11e-01  1.11e-01   1.95e-16  -1.37e-01  8.42e-17
52  -0.06590 -1.32e-01 -1.32e-01 -1.32e-01  -1.35e-16   1.00e-17  1.61e-01
53  -0.09656 -1.93e-01 -1.93e-01 -1.93e-01  -4.92e-16  -2.63e-16 -2.58e-16
54  -0.08120 -1.62e-01 -1.62e-01 -1.62e-01   3.52e-16   5.75e-16  5.51e-16
55  -0.76834 -2.12e-15 -2.54e-15 -2.49e-15   2.26e-15   5.44e-17  5.07e-17
56  -0.03543  7.64e-17  7.41e-17  7.15e-17  -7.30e-17   3.64e-17 -7.81e-19
57   0.04050 -3.63e-17 -1.23e-17 -5.84e-17   5.18e-17  -8.95e-17 -2.10e-17
58   0.16409 -2.17e-16 -1.08e-16 -7.89e-17   3.23e-16  -4.71e-17 -4.23e-17
59   0.07100 -1.66e-16 -1.28e-16 -1.02e-16  -6.80e-18  -1.08e-16 -8.75e-17
60   0.01012  5.74e-18  1.07e-18 -2.92e-18   2.70e-17  -3.02e-18  3.95e-18
61  -0.50260  6.03e-01 -2.39e-17 -7.57e-16  -7.39e-01  -7.39e-01 -7.39e-01
62  -0.09477 -5.69e-01 -5.60e-16 -1.63e-16  -6.96e-01   4.14e-16  3.76e-16
63  -0.08911 -5.35e-01  2.68e-16  2.98e-16  -8.56e-16  -6.55e-01 -5.03e-16
64   0.15023  9.01e-01 -8.79e-16 -2.32e-16  -5.55e-17  -4.45e-16  1.10e+00
65  -0.07799 -4.68e-01  2.69e-17 -1.95e-16  -5.04e-16  -3.30e-16 -1.84e-16
66   0.02027  1.22e-01 -3.63e-17  3.19e-17  -1.02e-16  -1.21e-16 -1.46e-16
67   0.16094  2.99e-16  3.04e-16  3.64e-16  -2.62e-16   4.22e-16  1.42e-16
68  -0.06354 -1.62e-16 -4.87e-16 -4.48e-16   3.86e-16  -4.34e-17  1.15e-16
69   0.01350 -4.95e-17 -2.89e-17 -5.05e-18   4.25e-17   1.73e-16  6.32e-17
70  -0.00675 -3.16e-17 -1.07e-17 -2.68e-17  -1.12e-17  -2.65e-18 -3.81e-17
71  -0.01688 -1.05e-16 -8.01e-17 -6.90e-17   6.53e-17   8.08e-17  4.80e-17
72   0.11029  1.67e-16  1.17e-16  2.28e-16  -1.82e-16  -3.70e-16 -6.12e-16
73   0.14386 -7.45e-17 -1.73e-01  1.83e-16   2.11e-01   2.11e-01  2.11e-01
74   0.02707  3.19e-16  1.62e-01  2.84e-16   1.99e-01  -6.05e-17 -1.71e-16
75  -0.02877  6.10e-17 -1.73e-01  7.23e-17  -1.22e-16  -2.11e-01 -7.74e-17
76  -0.04945  8.15e-17 -2.97e-01  1.59e-16   8.25e-17   1.92e-16 -3.63e-01
77   0.10832  8.16e-16  6.50e-01  5.58e-16   5.58e-16   3.14e-16  6.63e-16
78  -0.02367 -1.11e-17 -1.42e-01 -4.34e-17   1.94e-16   2.59e-16  3.43e-16
79   0.37170  4.06e-16  4.93e-16  5.40e-16  -8.43e-16  -3.98e-16 -6.51e-16
80   0.01858  3.95e-17  3.44e-17  3.17e-17  -2.08e-16  -8.25e-17 -5.09e-17
81   0.07616  9.83e-17  1.01e-16 -1.02e-16   2.58e-17   4.85e-16  1.33e-16
82   0.05470 -6.99e-17 -8.16e-17 -1.09e-16  -2.00e-16  -3.26e-16 -2.85e-16
83  -0.01688 -1.58e-17 -2.14e-17 -2.59e-17  -3.08e-17   1.06e-17  3.20e-18
84  -0.05822 -2.09e-16 -1.44e-16 -1.13e-16  -9.36e-17   7.27e-17 -1.28e-16
85  -0.16094 -1.24e-16 -1.45e-16  1.93e-01  -2.37e-01  -2.37e-01 -2.37e-01
86   0.02707  1.65e-16  1.89e-16  1.62e-01   1.99e-01  -6.03e-17  6.70e-17
87   0.14578 -5.53e-16 -2.18e-16  8.75e-01   0.00e+00   1.07e+00 -1.59e-16
88  -0.11628  5.96e-16  6.39e-16 -6.98e-01  -6.77e-16  -3.98e-16 -8.55e-01
89  -0.05999 -2.00e-17 -5.99e-17 -3.60e-01  -1.83e-16  -8.39e-17 -2.26e-16
90  -0.02367  1.25e-16  1.06e-16 -1.42e-01   1.32e-16   1.42e-16  1.17e-16
91  -0.10984  8.09e-16  8.66e-16  7.22e-16  -5.15e-16   2.02e-16  2.21e-16
92   0.03219 -4.00e-16 -5.02e-16 -5.39e-16   5.55e-16  -1.35e-16  2.01e-16
93  -0.07616 -4.07e-17 -9.51e-17  2.06e-31  -3.02e-16   6.61e-16  2.57e-16
94   0.00675 -4.54e-17 -2.15e-17 -1.95e-17  -9.12e-18   2.81e-18 -7.25e-17
95   0.05822 -8.71e-16 -9.88e-16 -6.38e-16   1.22e-16   1.41e-16  7.47e-17
96  -0.04423  7.58e-17  1.79e-16  2.04e-16  -5.53e-17  -1.20e-16  1.82e-17
   dfb.lgP.V dfb.lP.VI dfb.e2.2.P dfb.e2.3.P dfb.e2.4. dfb.ep1.1.II
1   7.67e-01  7.67e-01  -4.43e-01  -4.43e-01 -4.43e-01    -1.21e+00
2  -8.59e-17 -1.31e-17   1.58e-01   1.58e-01  1.58e-01    -4.34e-01
3   1.30e-16  1.36e-16  -7.88e-02  -7.88e-02 -7.88e-02    -5.07e-16
4  -7.88e-17 -1.17e-16   9.32e-02   9.32e-02  9.32e-02     6.03e-16
5   2.37e-01 -1.82e-16   1.37e-01   1.37e-01  1.37e-01    -2.81e-16
6   2.98e-16  1.99e-01   1.15e-01   1.15e-01  1.15e-01     7.58e-17
7  -2.71e-16  4.13e-16   3.62e-01   3.62e-01  3.62e-01     1.98e-01
8   4.79e-17  7.42e-17   5.01e-02   5.01e-02  5.01e-02    -2.74e-02
9   2.66e-17 -6.69e-17  -5.73e-02  -5.73e-02 -5.73e-02     1.28e-16
10 -3.27e-16  1.15e-16  -2.32e-01  -2.32e-01 -2.32e-01    -2.35e-16
11  6.81e-17 -9.14e-17  -1.00e-01  -1.00e-01 -1.00e-01     1.68e-17
12 -1.44e-18 -1.87e-18  -1.43e-02  -1.43e-02 -1.43e-02    -2.46e-17
13 -7.39e-01 -7.39e-01  -4.26e-01   5.32e-17  3.94e-16     2.34e-01
14  4.32e-16  3.02e-16   4.02e-01   6.87e-16  3.64e-16     2.20e-01
15 -6.94e-16 -6.19e-16   3.78e-01  -3.69e-16 -2.84e-16     6.28e-16
16  7.83e-16  1.36e-16  -6.37e-01   6.80e-16 -3.15e-16    -1.20e-15
17 -5.73e-01 -2.26e-16   3.31e-01   4.33e-16  3.22e-16     2.49e-16
18 -2.33e-16  1.49e-01  -8.60e-02   4.45e-17  6.15e-18    -1.45e-16
19 -1.08e-17 -6.60e-17   1.37e-01  -7.23e-17 -1.86e-17    -7.48e-02
20  9.01e-17  1.61e-16   2.70e-01   6.61e-17  2.67e-17     1.48e-01
21  5.45e-19  1.20e-17  -5.73e-02   2.49e-17  2.85e-17     9.44e-17
22 -4.01e-17 -4.37e-17   2.86e-02   2.03e-17  2.34e-17     4.81e-17
23  7.15e-17  1.42e-16   7.16e-02  -2.44e-17 -3.97e-17     1.26e-17
24 -1.82e-16 -3.79e-16  -4.68e-01   2.94e-16  2.44e-16    -3.61e-16
25  2.11e-01  2.11e-01  -1.77e-16   1.22e-01 -2.87e-16    -6.69e-02
26  2.93e-17 -1.05e-16  -3.11e-16  -1.15e-01 -2.69e-16    -6.29e-02
27 -9.78e-17 -6.32e-17   0.00e+00   1.22e-01  2.31e-18     3.07e-16
28  5.72e-17  1.40e-16   1.24e-16   2.10e-01  8.60e-17     4.04e-16
29  7.96e-01  4.42e-16  -8.12e-16  -4.60e-01 -7.34e-16     4.06e-16
30  2.36e-16 -1.74e-01  -7.88e-17   1.00e-01 -6.81e-17     6.89e-17
31 -7.53e-16 -6.10e-16   1.98e-16   3.15e-01 -1.62e-16    -1.73e-01
32 -1.13e-16 -1.08e-16  -6.50e-17  -7.88e-02 -6.37e-17    -4.32e-02
33  1.32e-16 -8.13e-17  -3.80e-17  -3.23e-01 -1.23e-16     2.92e-16
34 -2.85e-16 -3.39e-16  -1.82e-17  -2.32e-01 -9.79e-17    -5.64e-17
35  1.76e-17 -1.65e-17   2.81e-18   7.16e-02  1.83e-17    -1.36e-17
36 -1.33e-17  1.27e-16   3.20e-16   2.47e-01  1.35e-16     4.33e-16
37 -2.37e-01 -2.37e-01   5.49e-17   6.82e-17 -1.37e-01     7.48e-02
38  4.27e-17 -3.78e-17  -2.45e-16  -2.49e-16 -1.15e-01    -6.29e-02
39 -2.19e-16 -1.53e-16   4.09e-16   2.06e-16 -6.18e-01    -2.52e-16
40 -6.12e-16 -1.77e-16   2.50e-17  -4.11e-17  4.93e-01     1.41e-15
41 -4.41e-01 -5.13e-16   3.02e-16   2.76e-16  2.55e-01     3.52e-16
42  1.30e-16 -1.74e-01  -1.14e-16  -1.17e-16  1.00e-01     2.00e-16
43  7.58e-16  7.96e-17   1.05e-15   1.09e-15 -9.32e-02     2.55e-01
44 -1.78e-16 -1.81e-16  -5.24e-16  -5.91e-16 -1.37e-01    -3.74e-01
45 -1.44e-16 -6.97e-17   1.22e-16   2.15e-16  3.23e-01    -7.48e-16
46 -3.16e-17 -1.65e-17  -5.78e-17  -4.53e-17 -2.86e-02    -1.18e-17
47 -1.05e-15  4.98e-16  -6.31e-16  -6.99e-16 -2.47e-01    -3.62e-16
48  9.10e-17 -1.06e-16   6.16e-16   6.09e-16  1.88e-01     4.33e-16
49  7.67e-01  7.67e-01  -4.43e-01  -4.43e-01 -4.43e-01     7.28e-01
50 -2.90e-17  1.40e-16   1.58e-01   1.58e-01  1.58e-01     2.60e-01
51  1.34e-16  1.36e-16  -7.88e-02  -7.88e-02 -7.88e-02    -4.84e-16
52 -1.33e-16 -9.60e-17   9.32e-02   9.32e-02  9.32e-02     5.07e-16
53  2.37e-01 -2.35e-16   1.37e-01   1.37e-01  1.37e-01    -1.00e-16
54  3.92e-16  1.99e-01   1.15e-01   1.15e-01  1.15e-01     1.81e-16
55  8.88e-16  4.00e-16   3.62e-01   3.62e-01  3.62e-01     1.98e-01
56  1.99e-17  6.82e-17   5.01e-02   5.01e-02  5.01e-02    -2.74e-02
57  2.41e-17 -7.76e-17  -5.73e-02  -5.73e-02 -5.73e-02     4.43e-17
58  5.94e-17  1.23e-16  -2.32e-01  -2.32e-01 -2.32e-01    -5.23e-16
59  3.04e-17 -2.02e-16  -1.00e-01  -1.00e-01 -1.00e-01     3.99e-17
60  1.81e-17  7.09e-20  -1.43e-02  -1.43e-02 -1.43e-02    -4.03e-17
61 -7.39e-01 -7.39e-01  -4.26e-01  -2.85e-16 -7.30e-17     2.34e-01
62  3.50e-16  3.16e-16   4.02e-01   4.95e-16  1.80e-16     2.20e-01
63 -4.13e-16 -2.98e-16   3.78e-01  -2.74e-16 -1.29e-16     8.69e-16
64  1.30e-16 -1.68e-16  -6.37e-01   9.72e-16  2.68e-16    -5.64e-16
65 -5.73e-01 -1.27e-17   3.31e-01   3.09e-16  1.15e-16     3.84e-16
66 -1.52e-16  1.49e-01  -8.60e-02   1.40e-16  5.68e-17    -1.18e-16
67 -2.50e-17  2.39e-16   1.37e-01  -2.46e-16 -3.27e-16    -7.48e-02
68  5.24e-17 -1.74e-17   2.70e-01   3.66e-16  3.18e-16     1.48e-01
69  8.45e-18  4.24e-18  -5.73e-02   2.51e-17  5.11e-18     1.14e-16
70 -4.41e-17 -5.46e-17   2.86e-02   2.28e-17  3.03e-17     2.15e-17
71  9.93e-17  4.60e-17   7.16e-02   3.92e-17  4.12e-17    -3.06e-17
72 -3.52e-16 -4.42e-16  -4.68e-01   1.94e-16  2.11e-16    -1.95e-16
73  2.11e-01  2.11e-01   3.83e-17   1.22e-01 -1.63e-16    -6.69e-02
74 -1.14e-17 -8.17e-17  -3.47e-16  -1.15e-01 -3.25e-16    -6.29e-02
75 -1.21e-16 -3.72e-17  -5.27e-17   1.22e-01 -5.05e-17     3.32e-16
76  5.63e-17  1.50e-16  -2.47e-17   2.10e-01 -9.56e-17     3.46e-16
77  7.96e-01  3.87e-16  -7.22e-16  -4.60e-01 -5.57e-16     5.63e-16
78  2.60e-16 -1.74e-01  -1.10e-16   1.00e-01 -9.71e-17    -1.82e-17
79 -9.19e-16 -3.98e-16  -3.34e-16   3.15e-01 -5.61e-16    -1.73e-01
80 -4.85e-17 -7.95e-17  -4.02e-17  -7.88e-02 -4.95e-18    -4.32e-02
81  6.15e-17 -2.13e-16  -1.78e-16  -3.23e-01 -6.12e-18     1.87e-16
82 -2.85e-16 -2.97e-16  -4.55e-17  -2.32e-01 -1.42e-17    -5.64e-17
83  7.88e-18 -4.36e-18   1.12e-17   7.16e-02  2.28e-17    -1.55e-17
84  6.98e-17 -1.25e-16   2.33e-16   2.47e-01 -1.92e-17     3.53e-16
85 -2.37e-01 -2.37e-01   1.09e-16   1.02e-16 -1.37e-01     7.48e-02
86  2.67e-17 -1.24e-17  -2.70e-16  -2.96e-16 -1.15e-01    -6.29e-02
87 -1.95e-16  4.14e-17   2.98e-16  -5.15e-17 -6.18e-01    -4.97e-16
88 -5.83e-16 -4.24e-16  -2.48e-16  -1.64e-16  4.93e-01     1.20e-15
89 -4.41e-01 -2.02e-16   8.53e-17   1.06e-16  2.55e-01     1.42e-16
90  8.28e-17 -1.74e-01  -1.80e-16  -1.50e-16  1.00e-01     1.86e-16
91 -3.71e-16  2.25e-16  -8.97e-16  -8.69e-16 -9.32e-02    -1.53e-01
92  7.92e-17 -4.15e-17   3.04e-16   3.64e-16 -1.37e-01     2.24e-01
93 -2.68e-16 -8.07e-17  -3.65e-16  -2.96e-16  3.23e-01     7.71e-16
94  3.88e-18 -1.16e-18   9.00e-17   6.43e-17 -2.86e-02    -2.13e-17
95  8.98e-16 -2.62e-16   7.42e-16   5.96e-16 -2.47e-01    -3.74e-16
96 -2.27e-16 -7.04e-18  -6.68e-17  -1.56e-16  1.88e-01     2.24e-16
   dfb.ep2.1.II dfb.ep1.2.II dfb.ep2.2.II dfb.ep1.3.II dfb.ep2.3.II
1     -3.41e-15    -2.43e-01    -2.92e-15    -2.43e-01    -2.26e-15
2     -2.72e-15    -8.68e-02    -2.06e-15    -8.68e-02    -1.77e-15
3     -3.88e-17    -3.24e-16    -1.80e-16    -2.27e-16    -1.04e-16
4      5.41e-16     4.63e-16     4.13e-16     5.67e-16     3.46e-16
5     -2.58e-16    -1.54e-16    -2.77e-16    -2.28e-16    -3.39e-16
6      5.30e-16     1.40e-16     2.71e-16     9.15e-17     2.96e-16
7     -8.87e-01     1.98e-01     1.31e-15     1.98e-01     9.11e-16
8      1.23e-01    -2.74e-02    -2.21e-17    -2.74e-02    -8.40e-17
9      2.23e-16     1.20e-16     1.53e-16     9.07e-17     1.32e-16
10    -2.39e-16    -4.26e-16    -1.65e-16    -2.18e-16    -2.42e-16
11     2.50e-17    -3.29e-17     7.36e-17     5.03e-17     7.85e-17
12    -1.75e-17     3.68e-18    -1.32e-17    -2.38e-18    -1.69e-17
13    -3.40e-16     1.17e+00    -3.77e-16     2.34e-01    -6.05e-16
14    -2.52e-15     1.10e+00    -1.67e-15     2.20e-01    -1.63e-15
15    -2.81e-16     4.16e-16    -1.27e-16     4.42e-16    -5.65e-17
16    -1.30e-15    -1.53e-15    -1.60e-15    -1.30e-15    -8.14e-16
17     3.78e-16     1.47e-16     1.17e-16     2.72e-16     1.55e-16
18    -1.11e-16    -1.19e-16    -1.08e-16    -4.29e-17    -5.44e-17
19     1.63e-16    -7.48e-02     3.35e-01    -7.48e-02     1.41e-16
20     3.03e-16     1.48e-01    -6.60e-01     1.48e-01     5.22e-17
21     6.13e-17     1.05e-16     1.50e-16     9.25e-17     1.25e-16
22     8.77e-18     5.08e-17     2.44e-17     4.72e-17     2.17e-17
23    -5.33e-17    -6.35e-17    -4.64e-17    -7.26e-17     4.10e-18
24     4.48e-16     3.20e-16     3.51e-16     2.26e-16     3.84e-17
25    -2.43e-17    -6.69e-02     7.19e-17    -3.34e-01     1.73e-16
26     5.44e-16    -6.29e-02     4.33e-16    -3.14e-01     3.70e-16
27     2.33e-16     1.79e-16     1.80e-16     2.26e-16     1.05e-16
28     8.33e-16     4.17e-16     6.13e-16     4.92e-16     4.18e-16
29     9.64e-16     4.92e-16     9.59e-16     1.10e-15     9.36e-16
30     5.27e-17     9.91e-18     1.25e-16    -3.27e-17    -2.28e-17
31     0.00e+00    -1.73e-01     8.36e-17    -1.73e-01     7.73e-01
32     5.27e-17    -4.32e-02     6.50e-17    -4.32e-02     1.93e-01
33    -2.70e-16     3.90e-16     7.83e-17     3.60e-16     1.50e-16
34    -9.32e-17    -6.65e-17    -1.47e-16     1.54e-16    -1.28e-16
35    -9.40e-17    -4.03e-17    -1.03e-16    -5.23e-17    -1.06e-16
36    -7.87e-17     1.09e-16     1.78e-16    -5.17e-19     3.54e-17
37    -2.19e-16     7.48e-02    -2.89e-16     7.48e-02    -3.52e-16
38     5.85e-16    -6.29e-02     5.31e-16    -6.29e-02     4.15e-16
39    -1.42e-16     3.24e-16     2.49e-16     5.84e-16     5.72e-16
40     1.19e-15     1.10e-15     8.98e-16     1.21e-15     8.51e-16
41     2.61e-16     3.30e-16     2.00e-16     3.22e-16     9.74e-17
42     9.91e-17     1.03e-16     9.86e-17     1.70e-17     1.10e-16
43     2.28e-01     2.55e-01     2.28e-01     2.55e-01     2.28e-01
44    -3.35e-01    -3.74e-01    -3.35e-01    -3.74e-01    -3.35e-01
45     1.56e-15    -8.92e-16     1.83e-16    -5.29e-16    -3.16e-16
46    -5.87e-17    -3.39e-17    -3.61e-17    -2.47e-17    -2.93e-17
47    -2.75e-16    -4.12e-16    -1.70e-16    -2.41e-16    -1.94e-16
48    -2.16e-16     2.36e-16     3.38e-16     6.52e-18    -6.92e-17
49    -3.33e-15    -2.43e-01    -2.54e-15    -2.43e-01    -2.26e-15
50    -2.57e-15    -8.68e-02    -1.94e-15    -8.68e-02    -1.77e-15
51    -1.23e-16    -2.84e-16    -1.41e-16    -1.72e-16    -7.12e-17
52     5.43e-16     4.66e-16     4.08e-16     5.26e-16     3.23e-16
53    -1.14e-16     1.25e-18    -1.68e-16    -8.82e-17    -2.25e-16
54     3.11e-16     1.86e-16     2.30e-16     4.35e-17     2.56e-16
55     8.87e-01     1.98e-01     1.09e-15     1.98e-01     6.07e-16
56    -1.23e-01    -2.74e-02    -1.33e-17    -2.74e-02    -8.40e-17
57     2.41e-16     9.28e-17     1.50e-16     1.18e-16     1.30e-16
58    -2.75e-16    -5.43e-16    -2.01e-16    -3.92e-16    -2.74e-16
59     4.61e-17     5.02e-17     1.19e-16     1.06e-16     1.05e-16
60    -1.30e-17    -7.68e-18    -1.39e-17    -1.15e-17    -1.97e-17
61    -2.18e-16    -7.01e-01    -5.02e-16     2.34e-01    -5.78e-16
62    -2.20e-15    -6.61e-01    -1.47e-15     2.20e-01    -1.43e-15
63     7.61e-17     4.37e-16    -1.29e-16     3.22e-16     1.47e-16
64    -1.16e-15    -5.95e-16    -1.04e-15    -3.98e-16    -4.35e-16
65     5.88e-16     6.41e-16     4.06e-16     4.51e-16     2.77e-16
66    -9.70e-17    -6.66e-17    -9.20e-17    -6.15e-17    -4.89e-17
67     2.91e-17    -7.48e-02    -3.35e-01    -7.48e-02     1.67e-16
68     2.42e-16     1.48e-01     6.60e-01     1.48e-01     1.04e-16
69    -9.97e-18     1.06e-16     6.90e-17     1.14e-16     1.20e-16
70     1.95e-17     1.06e-17     1.26e-17     3.08e-17     1.07e-17
71     2.40e-18    -2.56e-17     1.52e-18    -6.33e-17     1.24e-17
72     3.11e-16     2.22e-16     5.51e-16     3.04e-16     7.11e-17
73     1.28e-16    -6.69e-02     1.80e-16     2.01e-01     1.18e-16
74     5.72e-16    -6.29e-02     3.79e-16     1.89e-01     4.52e-16
75     1.84e-16     2.42e-16     1.55e-16     1.71e-16     1.39e-16
76     8.44e-16     2.50e-16     6.21e-16     3.23e-16     4.31e-16
77     9.42e-16     7.40e-16     9.66e-16     8.15e-16     9.20e-16
78     3.87e-17    -4.58e-17    -8.48e-17    -1.25e-16     2.17e-18
79     2.24e-16    -1.73e-01     3.44e-16    -1.73e-01    -7.73e-01
80    -1.01e-17    -4.32e-02     3.48e-17    -4.32e-02    -1.93e-01
81    -2.74e-16     3.47e-16     1.51e-16     5.20e-16     3.86e-16
82    -9.84e-17    -1.73e-16    -1.72e-16    -3.80e-17    -2.08e-16
83    -1.37e-16    -5.27e-17    -1.16e-16    -8.34e-17    -2.12e-16
84    -1.34e-16     2.99e-18     7.89e-17     1.64e-17    -6.08e-17
85    -8.16e-17     7.48e-02    -4.02e-17     7.48e-02    -3.52e-17
86     5.68e-16    -6.29e-02     4.87e-16    -6.29e-02     2.96e-16
87    -3.04e-16    -1.60e-16    -1.72e-16    -2.00e-16     3.38e-17
88     6.37e-16     9.58e-16     7.33e-16     8.83e-16     3.84e-16
89     6.52e-17     1.26e-16     6.64e-17    -5.98e-17     9.86e-18
90     1.88e-16     1.05e-16     1.60e-16     7.60e-17     1.44e-16
91    -2.28e-01    -1.53e-01    -2.28e-01    -1.53e-01    -2.28e-01
92     3.35e-01     2.24e-01     3.35e-01     2.24e-01     3.35e-01
93    -8.33e-16     4.77e-16     1.63e-16     5.10e-16     3.93e-16
94     6.08e-18     5.38e-18    -8.71e-18     1.97e-17    -1.07e-17
95    -1.82e-16    -1.05e-16    -1.34e-17    -1.98e-16    -2.99e-16
96     2.97e-16     1.08e-16     1.98e-16     2.01e-16     2.80e-16
   dfb.ep1.4.II dfb.e1.1.III dfb.e2.1.III dfb.e1.2.III dfb.e2.2.III
1     -2.43e-01    -1.21e+00    -2.51e-15    -2.43e-01    -2.04e-15
2     -8.68e-02    -1.01e-15    -2.23e-15    -1.18e-15    -1.59e-15
3     -3.18e-16     2.16e-01    -2.70e-16     4.32e-02    -2.96e-16
4      5.17e-16     1.13e-16     3.37e-16     1.11e-16     2.28e-16
5     -1.42e-16    -7.09e-16    -2.30e-16    -3.50e-16    -3.04e-16
6      1.06e-16    -3.40e-16     3.29e-16    -1.47e-16     1.70e-16
7      1.98e-01     1.98e-01    -8.87e-01     1.98e-01     1.60e-15
8     -2.74e-02    -2.73e-16    -1.71e-16    -1.85e-16    -2.18e-16
9      1.01e-16     3.14e-02    -1.40e-01     3.14e-02     9.29e-17
10    -3.03e-16    -2.06e-16     1.77e-17    -4.73e-16    -2.38e-16
11     4.32e-17     2.51e-17    -1.17e-17     3.78e-18     1.21e-16
12    -1.51e-17    -2.02e-17    -1.48e-17     8.58e-18    -2.45e-17
13     2.34e-01     2.34e-01     3.47e-16     1.17e+00    -1.28e-16
14     2.20e-01    -1.68e-15    -1.77e-15    -1.36e-15    -1.09e-15
15     4.91e-16     2.07e-01     3.73e-16     1.04e+00     4.66e-16
16    -9.52e-16     9.14e-16    -8.16e-16    -4.35e-16    -2.33e-16
17     2.13e-16    -5.40e-16     5.49e-16     4.26e-17     1.06e-16
18    -3.49e-17     1.20e-16    -5.77e-17    -8.94e-17    -4.33e-17
19    -7.48e-02    -7.48e-02     2.32e-16    -7.48e-02     3.35e-01
20     1.48e-01    -3.59e-16    -1.41e-16    -3.53e-16     1.43e-17
21     1.27e-16    -3.14e-02     1.40e-16    -3.14e-02     1.40e-01
22     3.08e-17     1.28e-17     2.65e-17     2.22e-17     1.70e-17
23    -2.32e-17     3.92e-17    -3.37e-18     2.38e-17     4.72e-17
24     1.52e-16    -2.56e-16     1.74e-16     9.20e-17     9.98e-17
25    -6.69e-02    -6.69e-02     2.41e-16    -6.69e-02     2.49e-16
26    -6.29e-02     2.79e-16     4.48e-16     2.29e-16     2.70e-16
27     2.34e-16     6.69e-02     2.99e-16     6.69e-02     3.81e-16
28     4.28e-16    -1.79e-16     5.90e-16     3.93e-18     1.06e-16
29     4.85e-16     1.16e-15     1.23e-15     9.97e-16     1.07e-15
30    -3.54e-17    -1.23e-16    -4.53e-18    -4.96e-17    -2.75e-17
31    -1.73e-01    -1.73e-01     2.84e-16    -1.73e-01     1.14e-16
32    -4.32e-02     1.62e-16     5.35e-17     8.77e-17     7.30e-17
33     3.61e-16    -1.77e-01    -1.03e-16    -1.77e-01    -7.77e-17
34     1.41e-16    -8.47e-17    -2.88e-16    -1.96e-16    -2.31e-16
35    -6.29e-17    -7.29e-17    -1.45e-16    -6.03e-17    -1.31e-16
36     1.96e-16     4.42e-17    -1.37e-16    -2.02e-16     5.38e-17
37     3.74e-01     7.48e-02    -2.00e-16     7.48e-02    -3.69e-16
38    -3.14e-01     3.86e-16     4.91e-16     3.66e-16     4.42e-16
39     3.71e-16    -3.39e-01     4.49e-17    -3.39e-01     1.86e-16
40     8.08e-16     6.61e-16     9.19e-16     7.62e-16     5.97e-16
41     2.60e-16    -2.41e-16     5.60e-17    -2.56e-17     9.23e-18
42     1.05e-16     2.72e-17     7.46e-17     5.10e-17     5.74e-17
43     2.55e-01     2.55e-01     2.28e-01     2.55e-01     2.28e-01
44    -3.74e-01     6.90e-16     1.56e-16     3.43e-16     4.15e-16
45    -5.33e-16     8.85e-01     7.91e-01     8.85e-01     7.91e-01
46    -3.26e-17     7.59e-17    -1.05e-16     5.24e-18     1.56e-17
47    -4.00e-16     3.73e-16    -4.63e-16    -5.77e-17    -5.65e-17
48     7.10e-17     2.02e-16     3.62e-17     4.56e-16     1.79e-16
49    -2.43e-01     7.28e-01    -2.36e-15    -2.43e-01    -1.81e-15
50    -8.68e-02    -1.11e-15    -2.02e-15    -1.33e-15    -1.52e-15
51    -2.70e-16    -1.29e-01    -3.20e-16     4.32e-02    -3.27e-16
52     5.06e-16     1.19e-16     4.37e-16     1.71e-16     2.41e-16
53    -1.02e-17    -5.67e-16    -2.02e-16    -2.86e-16    -2.41e-16
54     8.55e-17    -3.66e-16     1.65e-16    -1.31e-16     8.99e-17
55     1.98e-01     1.98e-01     8.87e-01     1.98e-01     8.81e-16
56    -2.74e-02    -2.08e-16    -2.43e-16    -1.75e-16    -1.75e-16
57     8.11e-17     3.14e-02     1.40e-01     3.14e-02     6.20e-17
58    -4.94e-16    -3.82e-16    -3.70e-16    -5.48e-16    -3.41e-16
59     9.76e-17     1.30e-16    -7.92e-18     7.96e-17     1.12e-16
60    -1.95e-17    -1.89e-17    -2.42e-17     7.53e-18    -2.18e-17
61     2.34e-01     2.34e-01    -9.16e-16    -7.01e-01    -6.41e-16
62     2.20e-01    -1.32e-15    -1.68e-15    -1.22e-15    -1.06e-15
63     4.41e-16     2.07e-01     4.61e-16    -6.21e-01     2.27e-16
64    -3.50e-16     7.79e-16    -1.04e-16     3.80e-16    -1.59e-16
65     3.41e-16    -1.58e-16     2.86e-16     3.57e-16     1.66e-16
66    -2.35e-17     6.58e-17    -4.98e-17    -1.15e-17    -4.09e-17
67    -7.48e-02    -7.48e-02     3.57e-17    -7.48e-02    -3.35e-01
68     1.48e-01    -3.04e-16    -7.57e-17     1.27e-17     9.67e-17
69     9.63e-17    -3.14e-02     7.81e-17    -3.14e-02    -1.40e-01
70     2.08e-17    -1.75e-17     3.55e-17    -2.00e-18    -6.07e-18
71    -3.25e-17    -8.90e-17     3.96e-17     4.06e-18     2.35e-17
72     1.56e-16     2.97e-16     8.23e-17     1.74e-16     5.44e-16
73    -6.69e-02    -6.69e-02     5.67e-17    -6.69e-02     8.80e-17
74    -6.29e-02     1.85e-16     4.37e-16     2.47e-16     2.38e-16
75     2.18e-16     6.69e-02     3.97e-16     6.69e-02     3.89e-16
76     3.18e-16    -2.08e-17     6.35e-16     2.71e-17     2.38e-16
77     5.34e-16     1.13e-15     1.09e-15     9.83e-16     1.26e-15
78    -6.95e-17    -2.14e-16     1.35e-17    -1.40e-16    -9.11e-17
79    -1.73e-01    -1.73e-01     7.32e-17    -1.73e-01     6.06e-16
80    -4.32e-02     1.54e-16     4.31e-17     5.73e-17     8.41e-17
81     5.22e-16    -1.77e-01    -1.88e-17    -1.77e-01     1.26e-16
82     1.04e-17     1.27e-16    -3.87e-16    -1.52e-16    -2.41e-16
83    -2.86e-17    -1.43e-16    -8.41e-17    -1.02e-16    -1.29e-16
84     1.95e-16     6.66e-17    -8.80e-17    -1.47e-17     2.65e-17
85    -2.24e-01     7.48e-02    -1.78e-16     7.48e-02     5.33e-17
86     1.89e-01     3.51e-16     5.48e-16     4.01e-16     4.27e-16
87    -1.65e-16    -3.39e-01    -7.99e-16    -3.39e-01    -9.29e-16
88     9.28e-16     7.34e-16     4.82e-16     8.13e-16     7.77e-16
89     8.09e-17    -1.98e-16    -1.58e-16    -2.04e-16    -9.96e-17
90     1.66e-16     6.46e-17     1.63e-16     5.26e-17     1.34e-16
91    -1.53e-01    -1.53e-01    -2.28e-01    -1.53e-01    -2.28e-01
92     2.24e-01     2.59e-16     5.97e-16     4.66e-16     3.35e-16
93     4.47e-16    -5.31e-01    -7.91e-01    -5.31e-01    -7.91e-01
94     3.02e-18    -7.00e-17     2.01e-17    -1.87e-17    -3.68e-17
95     3.02e-17    -4.85e-16     8.03e-18    -2.27e-16    -1.34e-16
96     2.25e-16     3.66e-16     1.78e-16    -1.41e-17     3.86e-16
   dfb.e1.3.III dfb.e2.3.III dfb.e1.4.III dfb.e1.1.IV dfb.e2.1.IV dfb.e1.2.IV
1     -2.43e-01    -1.60e-15    -2.43e-01   -1.21e+00   -2.52e-15   -2.43e-01
2     -1.36e-15    -1.30e-15    -1.38e-15   -9.15e-16   -2.12e-15   -1.16e-15
3      4.32e-02    -3.06e-16     4.32e-02   -1.78e-16    1.86e-17   -1.46e-16
4      2.41e-16     9.90e-17     1.82e-16   -2.55e-01    5.80e-16   -5.10e-02
5     -3.80e-16    -3.90e-16    -3.62e-16   -7.38e-16   -3.50e-16   -3.61e-16
6     -1.16e-16     8.28e-17    -1.33e-16   -4.68e-16    3.98e-16   -1.13e-16
7      1.98e-01     9.54e-16     1.98e-01    1.98e-01   -8.87e-01    1.98e-01
8     -2.67e-16    -2.31e-16    -2.38e-16   -1.24e-16   -8.47e-17   -7.21e-17
9      3.14e-02     7.54e-17     3.14e-02    2.38e-16    1.87e-16    2.13e-16
10    -2.97e-16    -2.91e-16    -3.43e-16    1.27e-01   -5.68e-01    1.27e-01
11     2.11e-17     6.63e-17     2.30e-17    4.85e-17   -8.29e-17   -7.83e-18
12    -7.42e-19    -2.02e-17    -1.11e-17   -1.31e-17   -1.31e-17    1.01e-17
13     2.34e-01    -1.97e-16     2.34e-01    2.34e-01    2.56e-17    1.17e+00
14    -1.44e-15    -1.15e-15    -1.35e-15   -1.31e-15   -1.73e-15   -1.70e-15
15     2.07e-01     4.73e-16     2.07e-01    7.87e-17   -1.86e-16    2.74e-16
16    -3.07e-16    -1.70e-16     8.75e-17   -3.49e-01   -2.14e-15   -1.75e+00
17    -2.47e-17     1.31e-16     3.79e-17   -3.65e-16    2.44e-16   -4.42e-16
18     5.59e-17    -1.28e-17     2.10e-17   -6.46e-17   -8.12e-17   -8.97e-17
19    -7.48e-02     2.34e-16    -7.48e-02   -7.48e-02    3.89e-16   -7.48e-02
20    -1.57e-16    -2.48e-16    -2.24e-16    2.15e-17    2.77e-16    5.24e-17
21    -3.14e-02     1.09e-16    -3.14e-02    1.82e-16    1.18e-16    1.40e-16
22     2.72e-17     1.50e-17     1.36e-17    1.57e-02    7.29e-18    1.57e-02
23    -1.86e-17     4.19e-17     2.98e-17    3.15e-17   -2.06e-17   -5.73e-18
24     5.48e-17    -3.10e-17    -5.39e-17    1.93e-17    4.50e-16    5.43e-16
25    -3.34e-01     1.37e-16    -6.69e-02   -6.69e-02    1.34e-16   -6.69e-02
26     2.39e-16     2.90e-16     3.20e-16    2.87e-16    3.45e-16    1.12e-16
27     3.34e-01     2.73e-16     6.69e-02    1.22e-16    1.24e-16    1.88e-16
28     8.71e-17     1.59e-16     8.20e-17    1.15e-01    9.78e-16    1.15e-01
29     1.39e-15     9.61e-16     8.33e-16    1.31e-15    1.28e-15    9.77e-16
30    -1.15e-16    -6.60e-17    -1.08e-16   -1.95e-16   -7.82e-17   -1.07e-16
31    -1.73e-01     7.73e-01    -1.73e-01   -1.73e-01    1.09e-16   -1.73e-01
32     1.08e-16     3.58e-17     1.06e-16    1.57e-16    1.81e-17    2.10e-17
33    -1.77e-01     7.91e-01    -1.77e-01    4.61e-16   -9.54e-17    2.62e-16
34     4.67e-17    -1.81e-16     1.49e-17   -1.27e-01   -1.32e-16   -1.27e-01
35    -7.37e-17    -1.40e-16    -7.35e-17   -9.04e-17   -1.19e-16   -4.55e-17
36    -2.68e-16    -4.31e-18    -8.66e-17    2.97e-16    8.55e-18    1.68e-17
37     7.48e-02    -2.52e-16     3.74e-01    7.48e-02   -1.58e-16    7.48e-02
38     3.11e-16     3.59e-16     3.37e-16    3.07e-16    5.04e-16    3.02e-16
39    -3.39e-01     3.26e-16    -1.69e+00    1.33e-16    2.01e-16    2.99e-16
40     8.14e-16     7.93e-16     4.53e-16    2.70e-01    1.74e-15    2.70e-01
41    -5.39e-17    -4.58e-18    -1.47e-16    1.03e-16    2.08e-16    1.70e-16
42    -2.67e-17     1.07e-16     7.97e-17    3.63e-17   -2.22e-17    2.57e-18
43     2.55e-01     2.28e-01     2.55e-01    2.55e-01    2.28e-01    2.55e-01
44     3.72e-16     4.96e-16     4.18e-16    4.96e-16    1.80e-16    2.33e-16
45     8.85e-01     7.91e-01     8.85e-01   -7.27e-16    7.09e-17   -3.48e-16
46     1.95e-17    -3.36e-17     1.91e-17   -7.84e-02   -7.01e-02   -7.84e-02
47     8.41e-17    -3.22e-16     1.65e-17   -2.01e-16    3.51e-16   -1.64e-16
48     3.62e-17     9.90e-17     3.22e-16    6.83e-16    2.36e-18    3.80e-16
49    -2.43e-01    -1.63e-15    -2.43e-01    7.28e-01   -2.46e-15   -2.43e-01
50    -1.43e-15    -1.28e-15    -1.40e-15   -1.01e-15   -1.94e-15   -1.20e-15
51     4.32e-02    -2.39e-16     4.32e-02   -2.04e-16   -1.48e-17   -1.34e-16
52     2.67e-16     1.24e-16     2.14e-16    1.53e-01    6.06e-16   -5.10e-02
53    -3.22e-16    -3.54e-16    -2.70e-16   -5.86e-16   -2.09e-16   -3.01e-16
54    -2.33e-16     9.33e-17    -2.26e-16   -2.93e-16    1.94e-16   -1.13e-16
55     1.98e-01     9.54e-16     1.98e-01    1.98e-01    8.87e-01    1.98e-01
56    -2.10e-16    -2.10e-16    -2.21e-16   -1.00e-17   -7.47e-17   -1.00e-17
57     3.14e-02     1.02e-16     3.14e-02    1.70e-16    1.63e-16    2.22e-16
58    -5.10e-16    -4.11e-16    -4.89e-16    1.27e-01    5.68e-01    1.27e-01
59     9.97e-17     1.15e-16     1.36e-16    1.25e-16   -3.57e-17    6.50e-17
60    -8.44e-18    -1.79e-17    -8.01e-18   -1.55e-17   -1.95e-17    6.12e-18
61     2.34e-01    -3.09e-16     2.34e-01    2.34e-01   -5.88e-16   -7.01e-01
62    -1.26e-15    -1.03e-15    -1.22e-15   -1.09e-15   -1.61e-15   -1.26e-15
63     2.07e-01     5.48e-16     2.07e-01    6.07e-16   -1.63e-17   -1.83e-17
64     2.89e-16     2.43e-16     4.44e-16   -3.49e-01   -1.38e-15    1.05e+00
65     3.14e-16     2.09e-16     1.30e-16   -1.75e-16    2.88e-16    5.20e-17
66    -1.96e-17    -3.23e-17     4.51e-17   -5.03e-17   -7.30e-17   -2.92e-17
67    -7.48e-02     1.17e-16    -7.48e-02   -7.48e-02    1.97e-16   -7.48e-02
68     1.74e-16    -1.96e-16    -7.58e-17   -1.61e-17    2.00e-16    2.06e-16
69    -3.14e-02     1.02e-16    -3.14e-02    1.45e-16    1.13e-16    1.26e-16
70     1.45e-17     8.34e-18     1.12e-17    1.57e-02    2.66e-17    1.57e-02
71    -3.83e-17     4.78e-17    -5.55e-18   -3.70e-17    4.04e-17   -3.23e-17
72     4.47e-16    -1.63e-16     1.72e-16    1.43e-16    3.59e-16    5.00e-16
73     2.01e-01     6.43e-17    -6.69e-02   -6.69e-02    1.67e-16   -6.69e-02
74     3.24e-16     3.27e-16     3.02e-16    3.45e-16    4.09e-16    2.14e-16
75    -2.01e-01     3.62e-16     6.69e-02    9.30e-17    1.29e-16    2.55e-16
76     7.29e-17     1.59e-16     3.92e-17    1.15e-01    8.68e-16    1.15e-01
77     1.02e-15     1.09e-15     8.32e-16    1.58e-15    1.31e-15    7.01e-16
78    -2.62e-16    -9.36e-17    -2.06e-16   -3.51e-16   -1.12e-17   -2.01e-16
79    -1.73e-01    -7.73e-01    -1.73e-01   -1.73e-01    3.69e-16   -1.73e-01
80     1.04e-16     8.52e-17     9.22e-17    5.11e-17   -1.54e-17   -2.86e-17
81    -1.77e-01    -7.91e-01    -1.77e-01    1.20e-16   -3.20e-17    4.93e-17
82    -4.41e-17    -5.14e-16     2.08e-17   -1.27e-01   -3.34e-16   -1.27e-01
83    -1.28e-16    -1.77e-16    -1.11e-16   -8.33e-17   -1.80e-16   -5.26e-17
84    -1.33e-16    -1.14e-16     2.04e-16    2.89e-16   -1.06e-16    4.36e-17
85     7.48e-02     8.99e-17    -2.24e-01    7.48e-02   -1.51e-16    7.48e-02
86     3.68e-16     2.21e-16     3.95e-16    2.13e-16    5.19e-16    3.05e-16
87    -3.39e-01    -5.70e-16     1.02e+00   -3.81e-16   -4.80e-17    2.58e-16
88     7.71e-16     5.31e-16     8.89e-16    2.70e-01    8.87e-16    2.70e-01
89    -2.12e-16    -1.50e-16    -8.04e-17    3.02e-17   -2.10e-17    2.37e-18
90     4.37e-17     1.17e-16     9.90e-17    1.15e-16    1.30e-16    1.99e-17
91    -1.53e-01    -2.28e-01    -1.53e-01   -1.53e-01   -2.28e-01   -1.53e-01
92     4.44e-16     2.43e-16     4.24e-16   -1.58e-17    3.65e-16    7.77e-17
93    -5.31e-01    -7.91e-01    -5.31e-01    1.09e-16   -2.02e-16   -3.35e-16
94    -1.53e-17     8.92e-18    -2.69e-17    4.70e-02    7.01e-02    4.70e-02
95    -3.37e-16    -1.65e-16    -8.31e-17   -5.86e-17   -6.10e-16   -1.70e-16
96     3.61e-16     1.86e-16     1.07e-16   -9.60e-17    2.43e-16   -3.53e-17
   dfb.e2.2.IV dfb.e1.3.IV dfb.e2.3.IV dfb.e1.4.IV dfb.ep1.1.V dfb.ep2.1.V
1    -2.09e-15   -2.43e-01   -1.54e-15   -2.43e-01   -1.21e+00   -2.54e-15
2    -1.49e-15   -1.36e-15   -1.22e-15   -1.33e-15   -4.82e-16   -1.93e-15
3    -6.36e-17   -5.96e-17   -1.08e-17   -1.70e-16   -2.75e-16   -2.32e-17
4     5.50e-16   -5.10e-02    4.44e-16   -5.10e-02    4.88e-16    5.73e-16
5    -3.50e-16   -3.68e-16   -4.31e-16   -2.83e-16   -3.74e-01   -5.73e-16
6     1.13e-16   -1.63e-16    1.67e-16   -1.58e-16   -9.55e-17    4.93e-16
7     1.37e-15    1.98e-01    6.65e-16    1.98e-01    1.98e-01   -8.87e-01
8    -8.03e-17   -1.79e-16   -8.43e-17   -7.77e-17   -1.25e-16   -8.61e-17
9     1.82e-16    1.79e-16    1.90e-16    1.78e-16    1.42e-16    1.68e-16
10   -1.58e-16    1.27e-01   -2.84e-16    1.27e-01   -3.40e-16   -4.89e-16
11    8.39e-17   -2.65e-19    1.59e-17    1.52e-17    5.50e-02   -2.46e-01
12   -1.55e-17    2.45e-18   -2.14e-17   -1.00e-17   -2.32e-17   -1.56e-17
13    9.26e-17    2.34e-01   -4.06e-16    2.34e-01    2.34e-01   -1.63e-16
14   -9.66e-16   -1.61e-15   -1.05e-15   -1.50e-15   -9.91e-16   -1.78e-15
15   -1.02e-18    2.76e-16   -1.14e-17    2.44e-16    5.29e-16   -2.51e-16
16   -1.34e-15   -3.49e-01   -9.32e-16   -3.49e-01   -1.21e-15   -1.14e-15
17   -1.29e-16   -2.88e-16   -9.38e-17   -1.24e-16    1.81e-01    2.95e-16
18   -9.05e-17    2.67e-17   -1.19e-17    3.63e-17   -6.43e-17   -1.25e-16
19    3.35e-01   -7.48e-02    2.23e-16   -7.48e-02   -7.48e-02    3.54e-16
20    4.64e-16    2.54e-16    9.77e-17    6.12e-17    4.01e-17    1.30e-16
21    1.59e-16    1.28e-16    1.54e-16    1.52e-16    1.11e-16    8.95e-17
22   -7.01e-02    1.57e-02    3.89e-18    1.57e-02    4.62e-17    1.10e-17
23   -5.90e-18   -3.77e-17    4.20e-17    1.08e-17    3.92e-02   -1.00e-16
24    3.72e-16    6.13e-16    1.03e-16    4.79e-16   -1.01e-16    2.44e-16
25    1.52e-17   -3.34e-01    1.83e-16   -6.69e-02   -6.69e-02    2.21e-16
26    1.80e-16    1.41e-16    2.17e-16    3.06e-16   -2.96e-17    2.87e-16
27    1.30e-16    1.54e-16    7.73e-17    1.87e-16    3.70e-16    1.70e-16
28    7.03e-16    5.75e-01    4.99e-16    1.15e-01    3.14e-16    7.45e-16
29    1.03e-15    1.21e-15    9.84e-16    7.77e-16   -2.52e-01    1.89e-15
30    1.95e-17   -1.76e-16   -5.56e-17   -1.61e-16    3.41e-17    7.99e-17
31    4.89e-17   -1.73e-01    7.73e-01   -1.73e-01   -1.73e-01   -8.02e-17
32    2.17e-17    5.69e-17   -2.97e-17    4.86e-17    1.22e-16    2.85e-17
33    2.55e-16    2.80e-16    2.60e-16    3.14e-16    1.71e-16   -1.43e-16
34   -1.37e-16   -1.27e-01    5.68e-01   -1.27e-01   -2.71e-18   -1.19e-16
35   -6.72e-17   -3.31e-17   -1.25e-16   -3.69e-17    3.92e-02   -8.09e-17
36    1.32e-16   -3.30e-17   -1.41e-17    1.85e-16    2.34e-16    1.15e-16
37   -6.36e-17    7.48e-02   -2.23e-16    3.74e-01    7.48e-02   -2.17e-17
38    4.39e-16    2.70e-16    2.92e-16    2.89e-16    2.33e-16    4.62e-16
39    2.25e-16    7.02e-16    5.32e-16    3.52e-16   -1.48e-16   -6.51e-17
40    1.53e-15    2.70e-01    9.39e-16    1.35e+00    1.41e-15    1.17e-15
41    1.94e-16    1.89e-16   -1.05e-16    2.89e-16    1.39e-01    1.66e-16
42    1.02e-16   -7.24e-17    8.48e-17    1.09e-17    8.96e-17    5.47e-17
43    2.28e-01    2.55e-01    2.28e-01    2.55e-01    2.55e-01    2.28e-01
44    2.71e-16    3.35e-16    2.48e-16    2.33e-16    3.30e-16    1.42e-16
45   -1.77e-16   -2.37e-16   -1.71e-16   -2.49e-16    1.33e-16    2.15e-16
46   -7.01e-02   -7.84e-02   -7.01e-02   -7.84e-02   -1.49e-17   -7.25e-17
47   -2.47e-16   -7.07e-17   -7.00e-17   -2.82e-16   -6.76e-01   -6.05e-01
48    3.60e-16    1.42e-16    1.20e-16    2.14e-16    6.34e-16   -3.41e-17
49   -2.42e-15   -2.43e-01   -1.79e-15   -2.43e-01    7.28e-01   -3.04e-15
50   -1.39e-15   -1.36e-15   -1.21e-15   -1.27e-15   -5.03e-16   -1.75e-15
51   -3.44e-17   -7.88e-17   -2.70e-17   -1.53e-16   -3.58e-16   -7.16e-17
52    4.86e-16   -5.10e-02    3.80e-16   -5.10e-02    5.15e-16    6.12e-16
53   -3.21e-16   -4.03e-16   -3.81e-16   -3.53e-16    2.24e-01   -5.49e-16
54    7.53e-17   -2.31e-16    9.19e-17   -2.02e-16   -1.03e-19    2.30e-16
55    9.44e-16    1.98e-01    5.05e-16    1.98e-01    1.98e-01    8.87e-01
56   -4.43e-17    1.58e-17   -8.24e-17   -4.15e-17   -7.51e-17   -1.07e-16
57    1.63e-16    2.06e-16    1.68e-16    1.93e-16    1.34e-16    1.68e-16
58   -2.52e-16    1.27e-01   -3.47e-16    1.27e-01   -4.72e-16   -7.30e-16
59    1.46e-16    7.61e-17    9.20e-17    1.24e-16    5.50e-02    2.46e-01
60   -1.95e-17   -5.35e-18   -2.14e-17   -1.04e-17   -3.14e-17   -2.29e-17
61   -3.31e-16    2.34e-01   -5.07e-16    2.34e-01    2.34e-01   -8.41e-16
62   -9.78e-16   -1.35e-15   -9.93e-16   -1.21e-15   -6.86e-16   -1.63e-15
63   -1.02e-18    2.82e-16   -6.32e-18    2.24e-16    5.14e-16    4.27e-17
64   -1.11e-15   -3.49e-01   -4.98e-16   -3.49e-01   -9.13e-16   -1.10e-15
65    8.99e-18   -4.21e-18    6.24e-17   -1.82e-16    1.81e-01    4.42e-16
66   -1.13e-16   -3.90e-17   -5.75e-17   -5.41e-18   -5.63e-17   -3.77e-17
67   -3.35e-01   -7.48e-02    2.97e-16   -7.48e-02   -7.48e-02    1.41e-16
68    4.15e-16    3.52e-16    1.26e-16    1.76e-16    2.33e-18    1.19e-16
69    1.52e-16    1.16e-16    1.32e-16    1.16e-16    1.26e-16    1.09e-16
70    7.01e-02    1.57e-02   -1.17e-17    1.57e-02    3.59e-17    3.02e-17
71    1.21e-16   -4.26e-17    2.78e-17    5.82e-18    3.92e-02    3.07e-17
72    4.75e-16    6.39e-16    1.75e-16    5.85e-16   -1.79e-16    1.19e-16
73    1.52e-16    2.01e-01    1.83e-16   -6.69e-02   -6.69e-02    2.43e-16
74    2.37e-16    3.48e-16    2.85e-16    3.28e-16   -1.56e-17    3.12e-16
75    1.24e-16    1.21e-16    1.08e-16    1.89e-16    3.67e-16    2.00e-16
76    5.86e-16   -3.45e-01    4.85e-16    1.15e-01    4.23e-16    7.88e-16
77    1.42e-15    1.03e-15    1.19e-15    6.81e-16   -2.52e-01    1.86e-15
78   -4.40e-17   -2.38e-16   -6.69e-17   -2.21e-16   -4.62e-17    3.00e-17
79    0.00e+00   -1.73e-01   -7.73e-01   -1.73e-01   -1.73e-01    5.92e-16
80    1.56e-17    1.53e-17    3.62e-18    1.48e-17    5.28e-17    7.71e-18
81    1.70e-16    2.94e-16    1.70e-16    3.55e-16   -4.08e-17   -2.09e-16
82   -2.45e-16   -1.27e-01   -5.68e-01   -1.27e-01   -1.28e-17   -2.34e-16
83   -1.05e-16   -7.93e-17   -1.57e-16   -4.20e-17    3.92e-02   -2.08e-16
84    1.61e-16    5.25e-17    3.03e-17    2.86e-16    3.16e-16   -6.89e-17
85    1.70e-17    7.48e-02    1.86e-17   -2.24e-01    7.48e-02   -4.45e-16
86    3.85e-16    2.92e-16    2.39e-16    3.20e-16    1.79e-16    4.95e-16
87    6.05e-17    9.33e-17    3.04e-16    4.24e-16   -4.95e-16   -4.92e-17
88    8.73e-16    2.70e-01    6.04e-16   -8.11e-01    1.18e-15    4.72e-16
89    1.17e-16   -3.67e-17    6.94e-17    2.79e-18    1.39e-01   -3.56e-16
90    1.06e-16    1.54e-17    5.66e-17    6.28e-17    1.97e-16    1.06e-16
91   -2.28e-01   -1.53e-01   -2.28e-01   -1.53e-01   -1.53e-01   -2.28e-01
92    2.75e-16    5.60e-18    2.03e-16    1.30e-16    6.21e-17    3.42e-16
93    7.41e-17   -1.14e-17   -5.61e-17   -1.13e-16   -2.05e-17   -2.98e-16
94    7.01e-02    4.70e-02    7.01e-02    4.70e-02   -3.57e-17   -1.91e-17
95    9.12e-17   -1.96e-16   -2.31e-16    2.60e-16    4.06e-01    6.05e-01
96    3.30e-16    2.42e-16    1.98e-16    2.05e-16    2.12e-16    2.03e-16
   dfb.ep1.2.V dfb.ep2.2.V dfb.ep1.3.V dfb.ep2.3.V dfb.ep1.4.V dfb.e1.1.VI
1    -2.43e-01   -2.41e-15   -2.43e-01   -2.01e-15   -2.43e-01   -1.21e+00
2    -8.55e-16   -1.31e-15   -1.01e-15   -9.95e-16   -1.03e-15   -7.74e-16
3    -1.74e-16   -7.12e-17   -1.21e-16   -3.29e-17   -1.95e-16   -2.47e-16
4     3.58e-16    4.53e-16    5.37e-16    3.02e-16    4.23e-16    4.42e-16
5    -7.48e-02   -6.61e-16   -7.48e-02   -7.53e-16   -7.48e-02   -6.14e-16
6     5.42e-17    2.26e-16   -1.76e-17    2.64e-16    4.49e-17   -3.14e-01
7     1.98e-01    9.42e-16    1.98e-01    8.36e-16    1.98e-01    1.98e-01
8    -9.21e-17   -9.51e-17   -1.25e-16   -1.14e-16   -1.06e-16   -1.34e-16
9     1.33e-16    1.39e-16    1.10e-16    1.53e-16    1.28e-16    2.10e-16
10   -5.72e-16   -4.04e-16   -3.86e-16   -5.02e-16   -3.72e-16    2.24e-17
11    5.50e-02    1.65e-16    5.50e-02    1.67e-16    5.50e-02    2.11e-16
12    4.00e-18   -3.00e-17   -6.38e-18   -2.27e-17   -1.47e-17    7.84e-03
13    1.17e+00   -1.40e-17    2.34e-01   -7.69e-17    2.34e-01    2.34e-01
14   -1.36e-15   -9.39e-16   -1.40e-15   -8.98e-16   -1.18e-15   -8.66e-16
15    2.17e-16    3.84e-17    3.07e-16   -1.59e-16    2.50e-16    4.81e-16
16   -1.20e-15   -1.06e-15   -1.61e-15   -8.32e-16   -1.24e-15   -6.68e-16
17    9.06e-01    7.62e-17    1.81e-01    3.22e-16    1.81e-01   -4.17e-16
18   -1.27e-16   -4.30e-17    6.76e-17    1.31e-17    5.28e-17   -4.71e-02
19   -7.48e-02    3.35e-01   -7.48e-02    1.33e-16   -7.48e-02   -7.48e-02
20    7.88e-17    2.64e-16    7.15e-17   -1.35e-17   -5.17e-17    3.24e-17
21    1.02e-16    1.30e-16    9.81e-17    1.25e-16    1.23e-16    1.38e-16
22    5.21e-17    2.48e-17    5.95e-17    3.00e-17    4.06e-17    3.12e-17
23    3.92e-02   -1.75e-01    3.92e-02    1.55e-17    3.92e-02   -8.22e-17
24    3.11e-16    2.33e-16    2.95e-16    5.66e-18    2.88e-16   -2.56e-01
25   -6.69e-02    1.77e-16   -3.34e-01    1.76e-16   -6.69e-02   -6.69e-02
26   -2.74e-17    1.50e-16   -2.79e-18    1.14e-16    1.24e-16    2.00e-16
27    2.01e-16    2.16e-16    2.01e-16    1.37e-16    2.67e-16    2.03e-16
28    3.03e-16    4.73e-16    4.15e-16    3.90e-16    3.83e-16    1.26e-16
29   -2.52e-01    1.63e-15   -1.26e+00    1.66e-15   -2.52e-01    9.98e-16
30   -2.61e-17    2.57e-17   -3.95e-17    1.50e-17   -8.04e-17    5.50e-02
31   -1.73e-01    5.19e-17   -1.73e-01    7.73e-01   -1.73e-01   -1.73e-01
32    3.22e-17    3.55e-17    5.68e-17   -2.24e-17    6.47e-17    9.68e-17
33    1.08e-16    3.97e-17    1.23e-16   -7.86e-17    6.24e-17    3.42e-16
34   -1.49e-16   -1.46e-16    1.28e-16   -2.16e-16    6.88e-17    3.49e-16
35    3.92e-02   -1.11e-16    3.92e-02   -1.75e-01    3.92e-02   -9.45e-17
36    7.28e-17    1.65e-16   -7.06e-17    8.55e-17    4.14e-17    1.35e-01
37    7.48e-02   -4.49e-18    7.48e-02    7.88e-17    3.74e-01    7.48e-02
38    2.78e-16    3.80e-16    2.55e-16    2.45e-16    2.96e-16    3.48e-16
39    1.02e-16   -1.18e-16    2.24e-16    3.41e-16    2.18e-16   -1.18e-16
40    1.31e-15    1.03e-15    1.23e-15    8.56e-16    8.85e-16    9.56e-16
41    1.39e-01    8.38e-17    1.39e-01    0.00e+00    6.97e-01    1.45e-17
42    2.52e-17    2.45e-17   -4.83e-17    7.25e-17   -3.93e-17    5.50e-02
43    2.55e-01    2.28e-01    2.55e-01    2.28e-01    2.55e-01    2.55e-01
44    1.68e-16    2.28e-16    1.69e-16    2.46e-16    1.87e-16    3.19e-16
45   -3.14e-16    3.65e-17   -1.87e-18   -3.84e-16   -1.71e-16    3.20e-17
46   -5.14e-17   -4.25e-17   -2.87e-17   -5.17e-17   -3.66e-17   -5.22e-18
47   -6.76e-01   -6.05e-01   -6.76e-01   -6.05e-01   -6.76e-01   -8.16e-19
48    2.52e-16    1.96e-16    1.99e-17   -7.33e-17   -5.24e-17    5.14e-01
49   -2.43e-01   -2.32e-15   -2.43e-01   -2.43e-15   -2.43e-01    7.28e-01
50   -9.24e-16   -1.23e-15   -1.03e-15   -9.83e-16   -1.02e-15   -8.43e-16
51   -1.48e-16   -6.78e-17   -9.52e-17   -3.06e-17   -1.57e-16   -2.66e-16
52    4.16e-16    4.23e-16    5.16e-16    2.86e-16    4.97e-16    3.75e-16
53   -7.48e-02   -6.34e-16   -7.48e-02   -7.58e-16   -7.48e-02   -4.96e-16
54   -1.05e-18    2.11e-16   -9.41e-17    1.96e-16   -1.13e-16    1.89e-01
55    1.98e-01    8.11e-16    1.98e-01    3.13e-16    1.98e-01    1.98e-01
56   -3.25e-17   -8.18e-17   -8.43e-17   -1.15e-16   -8.54e-17   -1.10e-16
57    1.51e-16    1.42e-16    1.74e-16    1.38e-16    1.42e-16    2.00e-16
58   -8.63e-16   -4.94e-16   -6.91e-16   -6.65e-16   -7.05e-16   -7.15e-17
59    5.50e-02    1.98e-16    5.50e-02    2.06e-16    5.50e-02    2.95e-16
60   -4.63e-18   -2.81e-17   -1.79e-17   -3.30e-17   -2.64e-17    7.84e-03
61   -7.01e-01   -4.63e-16    2.34e-01   -2.46e-16    2.34e-01    2.34e-01
62   -1.19e-15   -9.03e-16   -1.14e-15   -7.99e-16   -1.07e-15   -9.65e-16
63   -9.02e-18   -7.58e-17    1.29e-16    5.98e-17    1.25e-16    2.01e-16
64   -6.49e-16   -1.03e-15   -6.46e-16   -3.44e-16   -9.98e-16   -3.24e-16
65   -5.44e-01    9.80e-17    1.81e-01    2.39e-16    1.81e-01   -1.96e-16
66    4.59e-17   -2.36e-17   -1.57e-17   -2.71e-17    2.72e-17   -4.71e-02
67   -7.48e-02   -3.35e-01   -7.48e-02    1.03e-16   -7.48e-02   -7.48e-02
68    1.78e-16    2.59e-16    2.42e-16    2.87e-17    7.09e-17    1.01e-16
69    9.44e-17    1.29e-16    9.99e-17    1.20e-16    1.04e-16    1.45e-16
70    4.76e-17    1.69e-17    4.24e-17    1.83e-17    4.12e-17    3.32e-17
71    3.92e-02    1.75e-01    3.92e-02    5.42e-17    3.92e-02   -1.18e-16
72    2.96e-16    8.21e-16    4.61e-16    1.65e-16    3.22e-16   -2.56e-01
73   -6.69e-02    1.61e-16    2.01e-01    1.58e-16   -6.69e-02   -6.69e-02
74    9.84e-17    1.06e-16    1.41e-16    1.39e-16    1.39e-16    9.38e-17
75    3.03e-16    2.25e-16    1.90e-16    1.90e-16    2.78e-16    2.10e-16
76    3.35e-16    5.46e-16    4.47e-16    3.60e-16    3.56e-16    2.20e-16
77   -2.52e-01    2.06e-15    7.55e-01    1.72e-15   -2.52e-01    9.66e-16
78   -4.87e-17   -4.99e-17   -1.24e-16   -3.25e-17   -1.44e-16    5.50e-02
79   -1.73e-01    2.70e-16   -1.73e-01   -7.73e-01   -1.73e-01   -1.73e-01
80   -2.55e-17    3.32e-17    2.72e-17    1.86e-17    3.17e-17    7.37e-17
81   -6.17e-18   -2.71e-17    2.65e-16    6.15e-17    2.31e-16    4.13e-16
82   -2.50e-16   -2.92e-16   -3.23e-17   -3.56e-16    5.73e-17    3.74e-16
83    3.92e-02   -1.74e-16    3.92e-02    1.75e-01    3.92e-02   -1.03e-16
84   -5.94e-17    1.03e-16    3.12e-17    1.17e-16    1.61e-16    1.35e-01
85    7.48e-02   -1.21e-16    7.48e-02   -1.58e-16   -2.24e-01    7.48e-02
86    2.78e-16    3.45e-16    2.73e-16    2.20e-16    3.13e-16    3.28e-16
87    3.74e-17   -9.44e-17    2.11e-17    9.84e-17    2.23e-16   -3.85e-16
88    6.99e-16    5.99e-16    7.72e-16    3.08e-16    6.67e-16    9.12e-16
89    1.39e-01   -1.34e-16    1.39e-01   -2.94e-16   -4.18e-01    2.98e-19
90    1.01e-16    9.87e-17    7.13e-17    1.08e-16    9.53e-17    5.50e-02
91   -1.53e-01   -2.28e-01   -1.53e-01   -2.28e-01   -1.53e-01   -1.53e-01
92    1.69e-16    1.72e-16    2.21e-16    1.71e-16    1.93e-16    2.14e-16
93   -1.11e-16   -9.89e-17    3.13e-17    2.78e-16    1.26e-16   -5.20e-17
94   -1.88e-17   -3.50e-17   -1.80e-17   -2.14e-17   -3.89e-17   -3.17e-17
95    4.06e-01    6.05e-01    4.06e-01    6.05e-01    4.06e-01    3.99e-17
96    2.02e-16    3.67e-16    3.80e-16    3.13e-16    4.09e-16   -3.08e-01
   dfb.e2.1.VI dfb.e1.2.VI dfb.e2.2.VI dfb.e1.3.VI dfb.e2.3.VI dfb.e1.4.VI
1    -1.74e-15   -2.43e-01   -2.10e-15   -2.43e-01   -1.95e-15   -2.43e-01
2    -2.13e-15   -1.00e-15   -1.56e-15   -1.23e-15   -1.19e-15   -1.24e-15
3     2.87e-17   -1.87e-16   -5.66e-17   -1.02e-16   -1.54e-17   -1.98e-16
4     5.25e-16    4.25e-16    4.08e-16    5.21e-16    3.52e-16    4.69e-16
5    -2.25e-16   -3.23e-16   -3.24e-16   -3.76e-16   -4.18e-16   -3.02e-16
6     2.70e-16   -6.29e-02    9.17e-17   -6.29e-02    1.05e-16   -6.29e-02
7    -8.87e-01    1.98e-01    1.22e-15    1.98e-01    7.39e-16    1.98e-01
8    -9.38e-17   -5.29e-17   -8.56e-17   -9.71e-17   -9.30e-17   -8.56e-17
9     1.92e-16    1.43e-16    1.06e-16    1.34e-16    1.19e-16    1.20e-16
10    2.56e-17   -5.42e-16    4.65e-17   -2.08e-16   -1.96e-16   -3.50e-16
11    9.79e-17    1.21e-16    1.65e-16    1.69e-16    6.88e-17    1.50e-16
12   -3.50e-02    7.84e-03   -1.55e-17    7.84e-03   -1.67e-17    7.84e-03
13    3.13e-16    1.17e+00   -4.94e-16    2.34e-01   -4.08e-16    2.34e-01
14   -1.92e-15   -1.09e-15   -9.54e-16   -1.32e-15   -8.57e-16   -1.03e-15
15   -3.30e-16    4.47e-16   -1.25e-16    5.57e-16   -2.53e-16    3.92e-16
16   -1.11e-15   -6.50e-16   -1.24e-15   -1.44e-15   -8.77e-16   -1.19e-15
17    1.84e-16    1.29e-16   -1.06e-16   -8.71e-17   -5.77e-17    2.25e-19
18   -1.01e-16   -2.36e-01    2.45e-17   -4.71e-02   -1.43e-17   -4.71e-02
19    1.75e-16   -7.48e-02    3.35e-01   -7.48e-02    1.48e-16   -7.48e-02
20    1.51e-16    2.16e-16    3.68e-16    3.04e-16    8.45e-17    1.26e-16
21    1.04e-16    8.47e-17    1.46e-16    9.96e-17    1.31e-16    1.28e-16
22    7.30e-18    4.78e-17    2.73e-17    5.25e-17    1.88e-17    3.50e-17
23   -1.24e-17   -3.37e-17    2.58e-18   -9.60e-17    3.33e-18   -4.75e-17
24    7.82e-16   -2.56e-01    1.15e+00   -2.56e-01    7.79e-17   -2.56e-01
25    1.66e-16   -6.69e-02    2.60e-16   -3.34e-01    2.59e-16   -6.69e-02
26    3.56e-16    1.18e-16    1.83e-16    1.44e-16    1.69e-16    1.90e-16
27    5.06e-17    1.71e-16    9.45e-17    1.53e-16    4.86e-17    1.64e-16
28    7.02e-16    2.83e-16    4.35e-16    4.52e-16    3.38e-16    3.76e-16
29    9.26e-16    7.89e-16    1.11e-15    1.11e-15    9.00e-16    7.01e-16
30   -7.56e-17    5.50e-02   -1.37e-16    2.75e-01   -1.05e-16    5.50e-02
31    7.53e-17   -1.73e-01    3.72e-16   -1.73e-01    7.73e-01   -1.73e-01
32    4.31e-17    1.96e-17    1.96e-17    5.03e-17   -4.67e-17    3.52e-17
33   -1.80e-17    2.58e-16    3.67e-16    3.17e-16    3.38e-16    3.09e-16
34    5.10e-18    1.14e-16    6.63e-18    2.38e-16   -8.45e-17    2.86e-16
35   -9.12e-17   -3.27e-17   -1.34e-16   -7.25e-17   -1.18e-16   -6.06e-17
36   -5.44e-17    1.35e-01    2.21e-16    1.35e-01   -6.05e-01    1.35e-01
37   -2.33e-16    7.48e-02   -1.95e-16    7.48e-02   -9.10e-17    3.74e-01
38    5.60e-16    3.54e-16    4.80e-16    3.28e-16    2.85e-16    3.77e-16
39    9.10e-17    2.49e-16   -5.83e-17    3.52e-16    7.48e-16    3.94e-16
40    1.55e-15    9.45e-16    1.03e-15    1.05e-15    1.08e-15    6.98e-16
41    7.61e-17    2.53e-16   -4.75e-18    1.21e-16   -1.87e-16    1.07e-16
42    1.05e-16    5.50e-02    8.78e-17    5.50e-02    1.67e-16    2.75e-01
43    2.28e-01    2.55e-01    2.28e-01    2.55e-01    2.28e-01    2.55e-01
44    1.78e-16    2.04e-16    2.28e-16    2.56e-16    2.61e-16    2.24e-16
45    2.12e-16   -2.81e-16    2.32e-17    2.08e-16   -2.46e-16   -7.48e-17
46   -5.09e-17   -2.83e-17   -1.23e-17   -3.17e-17   -3.03e-17   -4.48e-17
47   -3.11e-17   -3.36e-16    1.09e-16   -1.96e-16   -1.48e-16   -1.90e-16
48    4.60e-01    5.14e-01    4.60e-01    5.14e-01    4.60e-01    5.14e-01
49   -3.07e-15   -2.43e-01   -1.95e-15   -2.43e-01   -1.73e-15   -2.43e-01
50   -1.94e-15   -1.05e-15   -1.42e-15   -1.27e-15   -1.14e-15   -1.21e-15
51   -2.36e-17   -1.96e-16   -2.39e-17   -5.87e-17   -1.68e-17   -1.72e-16
52    5.16e-16    4.19e-16    4.32e-16    5.04e-16    3.51e-16    4.47e-16
53   -2.64e-16   -2.29e-16   -2.78e-16   -2.48e-16   -2.87e-16   -2.41e-16
54    3.79e-17   -6.29e-02    1.09e-17   -6.29e-02    3.82e-17   -6.29e-02
55    8.87e-01    1.98e-01    9.09e-16    1.98e-01    7.99e-16    1.98e-01
56   -9.55e-17   -4.42e-17   -8.64e-17   -8.27e-17   -9.14e-17   -8.41e-17
57    1.64e-16    1.53e-16    1.08e-16    1.53e-16    1.09e-16    1.20e-16
58   -2.42e-16   -5.56e-16   -1.19e-16   -3.83e-16   -2.19e-16   -3.31e-16
59    2.10e-16    1.99e-16    1.68e-16    2.28e-16    1.35e-16    2.02e-16
60    3.50e-02    7.84e-03   -1.85e-17    7.84e-03   -1.91e-17    7.84e-03
61   -1.02e-15   -7.01e-01   -2.84e-16    2.34e-01   -5.33e-17    2.34e-01
62   -1.82e-15   -1.07e-15   -8.13e-16   -1.23e-15   -8.01e-16   -9.88e-16
63   -2.36e-16    6.18e-17   -1.65e-16    8.07e-17    2.12e-16    1.82e-16
64   -9.56e-16   -7.27e-16   -1.04e-15   -4.59e-16   -6.22e-16   -6.35e-16
65    1.89e-16    1.68e-16    7.54e-17    1.85e-16    1.54e-16   -6.06e-17
66   -2.53e-17    1.41e-01   -1.14e-17   -4.71e-02   -7.16e-18   -4.71e-02
67    3.61e-16   -7.48e-02   -3.35e-01   -7.48e-02    2.79e-16   -7.48e-02
68    2.42e-16    3.78e-16    4.36e-16    5.08e-16    1.24e-16    2.87e-16
69    1.18e-16    9.30e-17    1.43e-16    8.66e-17    1.31e-16    8.90e-17
70    1.78e-17    4.62e-17    1.81e-17    5.88e-17    1.75e-17    5.57e-17
71   -3.99e-17   -4.13e-17   -1.10e-17   -9.86e-17   -8.69e-18   -5.01e-17
72    8.25e-16   -2.56e-01   -1.15e+00   -2.56e-01    5.26e-16   -2.56e-01
73    2.35e-16   -6.69e-02    1.02e-16    2.01e-01    1.22e-16   -6.69e-02
74    3.48e-16    1.10e-16    1.57e-16    1.80e-16    1.97e-16    1.80e-16
75    7.22e-17    2.05e-16    8.58e-17    8.46e-17    8.00e-17    1.48e-16
76    7.21e-16    2.97e-16    5.36e-16    4.55e-16    3.68e-16    3.00e-16
77    1.05e-15    6.91e-16    1.04e-15    9.47e-16    9.06e-16    5.76e-16
78   -8.85e-17    5.50e-02   -1.76e-16   -1.65e-01   -6.69e-17    5.50e-02
79    8.69e-16   -1.73e-01    4.38e-16   -1.73e-01   -7.73e-01   -1.73e-01
80    9.81e-18   -3.54e-18    2.82e-17    5.93e-17    1.17e-18    2.63e-17
81    8.09e-17    3.63e-16    3.45e-16    4.06e-16    1.91e-16    5.07e-16
82    4.11e-17    2.71e-18    5.17e-17    2.21e-16   -4.97e-18    3.15e-16
83   -1.72e-16   -4.76e-17   -1.28e-16   -1.12e-16   -1.31e-16   -8.36e-17
84   -6.80e-17    1.35e-01    2.02e-16    1.35e-01    6.05e-01    1.35e-01
85   -3.51e-16    7.48e-02   -1.84e-16    7.48e-02   -2.27e-16   -2.24e-01
86    5.85e-16    3.62e-16    4.52e-16    3.61e-16    2.65e-16    4.07e-16
87    5.79e-17    1.89e-16    9.28e-17   -4.63e-17    7.27e-16    2.39e-16
88    8.28e-16    8.70e-16    9.06e-16    9.29e-16    6.71e-16    6.80e-16
89   -2.41e-17   -6.71e-17   -9.56e-17   -2.33e-16   -1.73e-16   -1.79e-16
90    1.47e-16    5.50e-02    1.49e-16    5.50e-02    1.17e-16   -1.65e-01
91   -2.28e-01   -1.53e-01   -2.28e-01   -1.53e-01   -2.28e-01   -1.53e-01
92    4.33e-16    2.56e-16    2.57e-16    2.76e-16    2.21e-16    2.87e-16
93   -1.83e-16   -2.21e-16    3.29e-17    7.51e-17    1.83e-16    1.53e-16
94   -2.91e-17   -2.63e-17   -3.76e-17   -7.46e-18   -1.80e-17   -7.89e-18
95   -2.23e-16    1.51e-16    8.99e-17    5.81e-17   -6.54e-17    1.87e-16
96   -4.60e-01   -3.08e-01   -4.60e-01   -3.08e-01   -4.60e-01   -3.08e-01
   dfb.ep2.P.II dfb.e2.P.III dfb.e2.P.IV dfb.ep2.P.V dfb.e2.P.VI   dffit
1     -5.42e-01    -5.42e-01   -5.42e-01   -5.42e-01   -5.42e-01  2.5444
2     -1.94e-01    -1.91e-16   -2.72e-16    2.61e-18   -1.33e-16 -0.9099
3     -3.49e-16     9.65e-02   -1.73e-16   -2.34e-16   -2.52e-16  0.4527
4      3.35e-16     4.25e-17   -1.14e-01    1.89e-16    2.08e-16 -0.5354
5      2.27e-16    -1.17e-16    3.22e-17   -1.67e-01   -3.94e-17 -0.7845
6     -2.70e-16    -4.61e-16   -5.41e-16   -3.25e-16   -1.41e-01 -0.6597
7      4.44e-01     4.44e-01    4.44e-01    4.44e-01    4.44e-01  2.0807
8     -6.14e-02    -1.48e-16   -9.59e-17   -7.58e-17   -8.07e-17  0.2878
9     -2.56e-17     7.01e-02    6.50e-17   -1.30e-17    6.47e-17 -0.3290
10    -2.03e-16    -1.50e-16    2.84e-01   -4.86e-17   -4.02e-16 -1.3331
11    -4.66e-17    -7.84e-17   -2.36e-17    1.23e-01    1.09e-16 -0.5768
12     3.55e-18     9.79e-18    1.44e-17    9.53e-18    1.75e-02 -0.0822
13     5.22e-01     5.22e-01    5.22e-01    5.22e-01    5.22e-01 -2.4499
14     4.92e-01    -7.54e-16   -9.31e-16   -6.92e-16   -3.38e-16  2.3099
15     1.13e-15     4.63e-01    7.64e-16    8.85e-16    1.12e-15  2.1717
16    -3.12e-16     3.39e-16   -7.81e-01   -8.14e-16   -2.60e-16 -3.6614
17     2.03e-16    -3.11e-16   -3.38e-16    4.05e-01   -1.51e-16  1.9007
18     6.54e-17     1.76e-16    1.54e-16    1.58e-16   -1.05e-01 -0.4940
19    -1.67e-01    -1.67e-01   -1.67e-01   -1.67e-01   -1.67e-01 -0.7845
20     3.30e-01    -2.36e-16   -1.70e-16   -1.46e-16   -3.89e-17 -1.5487
21     6.40e-18    -7.01e-02    3.71e-17    1.66e-17   -1.38e-18  0.3290
22     5.19e-17     3.59e-17    3.51e-02    6.51e-17    6.88e-17 -0.1644
23    -5.86e-17    -4.26e-17   -5.06e-17    8.77e-02   -1.10e-16 -0.4115
24     6.07e-17     4.19e-17    4.06e-16    1.17e-16   -5.73e-01  2.6881
25    -1.50e-01    -1.50e-01   -1.50e-01   -1.50e-01   -1.50e-01  0.7012
26    -1.41e-01     1.26e-16    1.50e-16   -3.17e-17    8.01e-17 -0.6597
27     1.05e-16     1.50e-01    1.19e-16    1.62e-16    1.61e-16  0.7012
28    -6.36e-17    -2.79e-16    2.57e-01   -3.87e-18   -2.52e-17  1.2051
29    -7.40e-16    -2.47e-16   -2.89e-16   -5.63e-01   -3.65e-16 -2.6399
30    -5.42e-17    -1.46e-16   -2.44e-16   -1.42e-16    1.23e-01  0.5768
31    -3.86e-01    -3.86e-01   -3.86e-01   -3.86e-01   -3.86e-01 -1.8118
32    -9.65e-02     1.60e-16    1.38e-16    1.37e-16    9.66e-17  0.4527
33     3.49e-16    -3.96e-01    9.55e-17    5.85e-17    1.71e-16  1.8562
34     3.08e-16     4.15e-16   -2.84e-01    3.06e-16    3.79e-16  1.3331
35     4.94e-17     2.47e-17    2.25e-17    8.77e-02    2.24e-17 -0.4115
36     2.96e-16    -1.30e-16    1.88e-16    4.11e-17    3.03e-01 -1.4190
37     1.67e-01     1.67e-01    1.67e-01    1.67e-01    1.67e-01 -0.7845
38    -1.41e-01     1.01e-16    3.15e-17    4.12e-17    1.16e-16 -0.6597
39     3.45e-16    -7.57e-01    3.72e-16    1.98e-16    1.64e-16 -3.5529
40     7.10e-16     2.44e-16    6.04e-01    8.18e-16    1.78e-16  2.8341
41     4.15e-16     6.58e-18    2.20e-16    3.12e-01    4.28e-16  1.4621
42     4.66e-17    -3.90e-17   -8.11e-17    1.67e-17    1.23e-01  0.5768
43     1.14e-01     1.14e-01    1.14e-01    1.14e-01    1.14e-01  0.5354
44    -1.67e-01     3.06e-16    2.24e-16    1.03e-16    1.41e-16  0.7845
45    -8.66e-16     3.96e-01   -3.69e-16    7.25e-18    7.77e-18 -1.8562
46     2.63e-18     7.18e-17   -3.51e-02    1.13e-17   -6.88e-19  0.1644
47    -4.23e-16     1.90e-16   -3.30e-16   -3.03e-01   -4.75e-16  1.4190
48     7.83e-17     7.37e-17    5.37e-17   -1.56e-17    2.30e-01 -1.0781
49    -5.42e-01    -5.42e-01   -5.42e-01   -5.42e-01   -5.42e-01 -2.5444
50    -1.94e-01    -4.22e-16   -3.61e-16   -7.81e-17   -2.55e-16  0.9099
51    -3.23e-16     9.65e-02   -1.64e-16   -2.02e-16   -2.29e-16 -0.4527
52     2.73e-16    -7.08e-18   -1.14e-01    2.07e-16    1.77e-16  0.5354
53     3.35e-16    -2.36e-17   -3.22e-17   -1.67e-01    7.55e-17  0.7845
54    -2.65e-16    -5.73e-16   -5.74e-16   -4.78e-16   -1.41e-01  0.6597
55     4.44e-01     4.44e-01    4.44e-01    4.44e-01    4.44e-01 -2.0807
56    -6.14e-02    -1.10e-16    7.30e-18   -3.50e-17   -6.26e-17 -0.2878
57    -5.12e-17     7.01e-02    8.91e-17    3.55e-17    9.36e-17  0.3290
58    -4.47e-16    -2.03e-16    2.84e-01   -2.15e-16   -3.57e-16  1.3331
59    -5.88e-18     7.29e-17    4.73e-17    1.23e-01    1.50e-16  0.5768
60    -1.99e-17     2.32e-18   -2.52e-18   -1.43e-17    1.75e-02  0.0822
61     5.22e-01     5.22e-01    5.22e-01    5.22e-01    5.22e-01  2.4499
62     4.92e-01    -6.00e-16   -6.59e-16   -5.70e-16   -4.54e-16 -2.3099
63     9.57e-16     4.63e-01    7.14e-16    6.04e-16    5.54e-16 -2.1717
64     4.16e-16     7.75e-16   -7.81e-01   -3.02e-16    4.60e-17  3.6614
65     2.20e-16     7.38e-17   -2.08e-16    4.05e-01   -2.15e-16 -1.9007
66     4.47e-17     7.93e-17    9.57e-17    6.44e-17   -1.05e-01  0.4940
67    -1.67e-01    -1.67e-01   -1.67e-01   -1.67e-01   -1.67e-01  0.7845
68     3.30e-01    -2.32e-17    3.97e-17    4.80e-17    2.14e-16  1.5487
69     1.49e-17    -7.01e-02   -1.43e-18    1.16e-17   -4.13e-18 -0.3290
70     2.35e-17     5.44e-18    3.51e-02    5.50e-17    7.36e-17  0.1644
71    -1.05e-16    -1.11e-16   -9.56e-17    8.77e-02   -1.26e-16  0.4115
72    -4.37e-17     1.45e-16    4.30e-16    7.79e-17   -5.73e-01 -2.6881
73    -1.50e-01    -1.50e-01   -1.50e-01   -1.50e-01   -1.50e-01 -0.7012
74    -1.41e-01     1.36e-16    2.26e-16    4.83e-17    9.66e-17  0.6597
75     1.05e-16     1.50e-01    1.09e-16    1.47e-16    8.51e-17 -0.7012
76    -2.98e-16    -3.59e-16    2.57e-01   -9.36e-17   -1.26e-16 -1.2051
77    -3.93e-16    -6.60e-17   -6.13e-16   -5.63e-01   -2.98e-16  2.6399
78    -1.38e-16    -2.75e-16   -3.06e-16   -1.84e-16    1.23e-01 -0.5768
79    -3.86e-01    -3.86e-01   -3.86e-01   -3.86e-01   -3.86e-01  1.8118
80    -9.65e-02     1.08e-16    6.08e-17    5.36e-17    7.77e-17 -0.4527
81     3.49e-16    -3.96e-01    7.33e-17    1.18e-16    3.50e-16 -1.8562
82     1.66e-16     3.53e-16   -2.84e-01    3.15e-16    3.07e-16 -1.3331
83     6.67e-17     8.52e-18    4.50e-17    8.77e-02    2.93e-17  0.4115
84     3.27e-16     8.37e-17    3.45e-16    1.03e-16    3.03e-01  1.4190
85     1.67e-01     1.67e-01    1.67e-01    1.67e-01    1.67e-01  0.7845
86    -1.41e-01     1.58e-16    2.75e-17    3.16e-17    9.66e-17  0.6597
87    -1.38e-16    -7.57e-01    2.03e-16    1.74e-16   -1.93e-16  3.5529
88     8.21e-16     5.25e-16    6.04e-01    6.35e-16    5.10e-16 -2.8341
89     8.83e-17     2.97e-17    7.99e-17    3.12e-01    9.18e-17 -1.4621
90    -8.33e-17    -1.27e-16   -1.16e-16   -4.18e-17    1.23e-01 -0.5768
91     1.14e-01     1.14e-01    1.14e-01    1.14e-01    1.14e-01 -0.5354
92    -1.67e-01     2.19e-16   -1.78e-16    4.57e-17    8.86e-17 -0.7845
93     6.74e-16     3.96e-01   -6.44e-17    1.83e-16    2.33e-17  1.8562
94     3.34e-17    -2.50e-17   -3.51e-02    7.15e-18    8.94e-18 -0.1644
95    -2.06e-16    -2.50e-16   -1.36e-16   -3.03e-01    6.53e-17 -1.4190
96    -2.96e-17     1.56e-16   -5.79e-17    3.13e-16    2.30e-01  1.0781
      cov.r   cook.d   hat inf
1  5.09e-02 0.092127 0.688   *
2  1.28e+01 0.012809 0.688   *
3  2.43e+01 0.003202 0.687   *
4  2.23e+01 0.004473 0.687   *
5  1.59e+01 0.009554 0.688   *
6  1.91e+01 0.006775 0.688   *
7  3.94e-01 0.063544 0.687   *
8  2.75e+01 0.001297 0.687   *
9  2.68e+01 0.001694 0.688   *
10 4.89e+00 0.027101 0.687    
11 2.13e+01 0.005187 0.687   *
12 2.98e+01 0.000106 0.687   *
13 7.94e-02 0.085987 0.688   *
14 1.50e-01 0.077173 0.687   *
15 2.71e-01 0.068837 0.687   *
16 1.02e-04 0.173640 0.688   *
17 7.91e-01 0.053593 0.688    
18 2.33e+01 0.003811 0.688   *
19 1.59e+01 0.009554 0.688   *
20 2.62e+00 0.036231 0.687    
21 2.68e+01 0.001694 0.688   *
22 2.92e+01 0.000423 0.688   *
23 2.52e+01 0.002647 0.688   *
24 2.52e-02 0.101733 0.688   *
25 1.81e+01 0.007649 0.687   *
26 1.91e+01 0.006775 0.688   *
27 1.81e+01 0.007649 0.688   *
28 6.79e+00 0.022258 0.687    
29 3.20e-02 0.098478 0.687   *
30 2.13e+01 0.005187 0.687   *
31 1.09e+00 0.048935 0.687    
32 2.43e+01 0.003202 0.688   *
33 9.32e-01 0.051237 0.687    
34 4.89e+00 0.027101 0.688    
35 2.52e+01 0.002647 0.688   *
36 3.86e+00 0.030594 0.687    
37 1.59e+01 0.009554 0.687   *
38 1.91e+01 0.006775 0.688   *
39 2.01e-04 0.165171 0.687   *
40 1.20e-02 0.111817 0.687   *
41 3.41e+00 0.032420 0.687    
42 2.13e+01 0.005187 0.688   *
43 2.23e+01 0.004473 0.688   *
44 1.59e+01 0.009554 0.687   *
45 9.32e-01 0.051237 0.688   *
46 2.92e+01 0.000423 0.688   *
47 3.86e+00 0.030594 0.687    
48 9.11e+00 0.017891 0.688   *
49 5.09e-02 0.092127 0.688   *
50 1.28e+01 0.012809 0.688   *
51 2.43e+01 0.003202 0.688   *
52 2.23e+01 0.004473 0.687   *
53 1.59e+01 0.009554 0.687   *
54 1.91e+01 0.006775 0.688   *
55 3.94e-01 0.063544 0.688    
56 2.75e+01 0.001297 0.687   *
57 2.68e+01 0.001694 0.688   *
58 4.89e+00 0.027101 0.688    
59 2.13e+01 0.005187 0.687   *
60 2.98e+01 0.000106 0.688   *
61 7.94e-02 0.085987 0.688   *
62 1.50e-01 0.077173 0.687    
63 2.71e-01 0.068837 0.687    
64 1.02e-04 0.173640 0.688   *
65 7.91e-01 0.053593 0.687    
66 2.33e+01 0.003811 0.688   *
67 1.59e+01 0.009554 0.687   *
68 2.62e+00 0.036231 0.688    
69 2.68e+01 0.001694 0.688   *
70 2.92e+01 0.000423 0.687   *
71 2.52e+01 0.002647 0.688   *
72 2.52e-02 0.101733 0.687   *
73 1.81e+01 0.007649 0.688   *
74 1.91e+01 0.006775 0.687   *
75 1.81e+01 0.007649 0.688   *
76 6.79e+00 0.022258 0.687    
77 3.20e-02 0.098478 0.688    
78 2.13e+01 0.005187 0.688   *
79 1.09e+00 0.048935 0.688    
80 2.43e+01 0.003202 0.688   *
81 9.32e-01 0.051237 0.687    
82 4.89e+00 0.027101 0.688    
83 2.52e+01 0.002647 0.687   *
84 3.86e+00 0.030594 0.688    
85 1.59e+01 0.009554 0.688   *
86 1.91e+01 0.006775 0.687   *
87 2.01e-04 0.165171 0.688   *
88 1.20e-02 0.111817 0.688    
89 3.41e+00 0.032420 0.687    
90 2.13e+01 0.005187 0.687   *
91 2.23e+01 0.004473 0.688   *
92 1.59e+01 0.009554 0.688   *
93 9.32e-01 0.051237 0.687    
94 2.92e+01 0.000423 0.688   *
95 3.86e+00 0.030594 0.688    
96 9.11e+00 0.017891 0.688   *
influenceIndexPlot(modelo.dbca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dbca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1      -0.1803460      2.326312  0.9816
   2      -0.1687012      2.289458  0.8588
   3       0.1049524      1.741018  0.2268
   4      -0.1833730      2.300260  0.4484
   5      -0.3425549      2.612652  0.0452
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dbca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dbca
DW = 2.3263, p-value < 2.2e-16
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.dbca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dbca)
W = 0.99205, p-value = 0.8432
ad.test(rstudent(modelo.dbca))

    Anderson-Darling normality test

data:  rstudent(modelo.dbca)
A = 0.26803, p-value = 0.6771
lillie.test(rstudent(modelo.dbca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dbca)
D = 0.065238, p-value = 0.4014
ks.test(rstudent(modelo.dbca), "pnorm",
        alternative = "two.sided")

    Exact one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dbca)
D = 0.058852, p-value = 0.874
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dbca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dbca)
W = 0.04972, p-value = 0.5106
pearson.test(rstudent(modelo.dbca))

    Pearson chi-square normality test

data:  rstudent(modelo.dbca)
P = 13.687, p-value = 0.1877
sf.test(rstudent(modelo.dbca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dbca)
W = 0.99385, p-value = 0.8867

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dbca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 0.9637412, Df = 1, p = 0.32625
bptest(modelo.dbca)

    studentized Breusch-Pagan test

data:  modelo.dbca
BP = 96, df = 65, p-value = 0.007467
bptest(modelo.dbca, studentize = F)

    Breusch-Pagan test

data:  modelo.dbca
BP = 76.736, df = 65, p-value = 0.1513
olsrr::ols_test_breusch_pagan(modelo.dbca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

              Data               
 --------------------------------
 Response : rdto 
 Variables: fitted values of rdto 

        Test Summary         
 ----------------------------
 DF            =    1 
 Chi2          =    0.9637412 
 Prob > Chi2   =    0.3262461 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dbca %>% gvlma()

Análisis de varianza

\[Y_{ijkl} = \mu + \tau_{i} + \beta_{j} + \gamma_{k} + (\tau\beta)_{ij} + (\tau\gamma)_{ik} + (\beta\gamma)_{jk} + (\tau\beta\gamma)_{ijk} + \text{Error}(\gamma\text{Bloque})_{k(l)} \text{Error}(\tau\beta\text{Bloque})_{ij(l)} + \text{Error}(\tau\gamma\text{Bloque})_{ik(l)} + \delta_{l} + \epsilon_{ijk}\] \[\hat{Y}_{ijkl} = \mu + \tau_{i} + \beta_{j} + \gamma_{k} + (\tau\beta)_{ij} + (\tau\gamma)_{ik} + (\beta\gamma)_{jk} + (\tau\beta\gamma)_{ijk} + \text{Error}(\tau\beta\text{Bloque})_{ij(l)} + \text{Error}(\tau\gamma\text{Bloque})_{ik(l)} + \delta_{l}\]

Dónde:

\(Y_{ijkl}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijkl}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor epoca.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor linaje.

\(\gamma_{k}\) = Efecto del k-ésimo nivel del factor lugar.

\(\text{Error}(\gamma\text{Bloque})_{k(l)}\) = Efecto del k-ésimo nivel de lugar en el l-ésimo nivel de Bloque.

\(\text{Error}(\tau\beta\text{Bloque})_{ij(l)}\) = Efecto del i-ésimo nivel de epoca y el j-ésimo nivel de linaje en el l-ésimo nivel de Bloque.

\(\text{Error}(\tau\gamma\text{Bloque})_{ik(l)}\) = Efecto del i-ésimo nivel de epoca y el k-ésimo nivel de lugar en el l-ésimo nivel de Bloque.

\((\tau\beta)_{ij}\) = Efecto de la interacción entre el i-ésimo nivel del factor época y el j-ésimo nivel del factor linaje.

\((\tau\gamma)_{ik}\) = Efecto de la interacción entre el i-ésimo nivel del factor época y el k-ésimo nivel del factor lugar.

\((\beta\gamma)_{jk}\) = Efecto de la interacción entre el j-ésimo nivel del factor linaje y el k-ésimo nivel del factor lugar.

\((\tau\beta\gamma)_{ijk}\) = Efecto de la interacción entre el i-ésimo nivel del factor época, el j-ésimo nivel del factor linaje y el k-ésimo nivel del factor lugar

\(\delta_{l}\) = Efecto del k-ésimo nivel de Bloque.

\(\epsilon_{ijkl}\) = Residuo observado del modelo.

Pruebas de hipótesis

Para el factor A (epoca):

\(H_0: \tau_{A1} = \tau_{A2} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (linaje):

\(H_0: \beta_{B1} = \beta_{B2} = \beta_{B3} = \beta_{B4} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Para el factor C (lugar):

\(H_0: \gamma_{C1} = \gamma_{C2} = 0\)

\(H_1: \text{En al menos un nivel del factor C el } \gamma \text{ es diferente a los demás.}\)

\(H_1: \gamma_k \neq 0\text{; en al menos un nivel del factor C.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dbca, test = "F")
Analysis of Variance Table

Response: rdto
                    Df Sum Sq Mean Sq F value    Pr(>F)    
epoca                1 495.04  495.04 70.7483 2.184e-09 ***
linaje               3 149.21   49.74  7.1080 0.0009559 ***
lugar                1 580.17  580.17 82.9139 3.869e-10 ***
bloque               5 174.71   34.94  4.9936 0.0019117 ** 
epoca:linaje         3  13.54    4.51  0.6451 0.5921233    
epoca:lugar          1   6.00    6.00  0.8575 0.3618338    
linaje:lugar         3  99.08   33.03  4.7201 0.0081633 ** 
lugar:bloque         5 113.83   22.77  3.2537 0.0182692 *  
epoca:linaje:lugar   3  20.25    6.75  0.9647 0.4222083    
epoca:linaje:bloque 35 367.46   10.50  1.5004 0.1301777    
epoca:lugar:bloque   5  14.75    2.95  0.4216 0.8299374    
Residuals           30 209.92    7.00                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
GAD::estimates(modelo.dbca)
$tm
                    epoca linaje lugar bloque        n
epoca                   0      4     2      6 1.454545
linaje                  2      0     2      6 1.454545
lugar                   2      4     0      6 1.454545
bloque                  2      4     2      1 1.454545
epoca:linaje            0      0     2      6 1.454545
epoca:lugar             0      4     0      6 1.454545
linaje:lugar            2      0     0      6 1.454545
lugar:bloque            2      4     0      1 1.454545
epoca:linaje:lugar      0      0     0      6 1.454545
epoca:linaje:bloque     1      1     2      1 1.454545
epoca:lugar:bloque      0      4     0      1 1.454545
Res                     1      1     1      1 1.000000

$mse
                    Mean square estimates                     
epoca               "Res + epoca:linaje:bloque + epoca"       
linaje              "Res + epoca:linaje:bloque + linaje"      
lugar               "Res + lugar:bloque + lugar"              
bloque              "Res + epoca:linaje:bloque + bloque"      
epoca:linaje        "Res + epoca:linaje:bloque + epoca:linaje"
epoca:lugar         "Res + epoca:lugar:bloque + epoca:lugar"  
linaje:lugar        "Res + linaje:lugar"                      
lugar:bloque        "Res + lugar:bloque"                      
epoca:linaje:lugar  "Res + epoca:linaje:lugar"                
epoca:linaje:bloque "Res + epoca:linaje:bloque"               
epoca:lugar:bloque  "Res + epoca:lugar:bloque"                
Residual            "Res"                                     

$f.versus
                    F-ratio versus       
epoca               "epoca:linaje:bloque"
linaje              "epoca:linaje:bloque"
lugar               "lugar:bloque"       
bloque              "epoca:linaje:bloque"
epoca:linaje        "epoca:linaje:bloque"
epoca:lugar         "epoca:lugar:bloque" 
linaje:lugar        "Residual"           
lugar:bloque        "Residual"           
epoca:linaje:lugar  "Residual"           
epoca:linaje:bloque "Residual"           
epoca:lugar:bloque  "Residual"           
GAD::gad(modelo.dbca)
Analysis of Variance Table

Response: rdto
                    Df Sum Sq Mean Sq F value   Pr(>F)    
epoca                1 495.04  495.04 47.1522 5.68e-08 ***
linaje               3 149.21   49.74  4.7373 0.007077 ** 
lugar                1 580.17  580.17 25.4832 0.003940 ** 
bloque               5 174.71   34.94  3.3282 0.014571 *  
epoca:linaje         3  13.54    4.51  0.4299 0.732827    
epoca:lugar          1   6.00    6.00  2.0339 0.213159    
linaje:lugar         3  99.08   33.03  4.7201 0.008163 ** 
lugar:bloque         5 113.83   22.77  3.2537 0.018269 *  
epoca:linaje:lugar   3  20.25    6.75  0.9647 0.422208    
epoca:linaje:bloque 35 367.46   10.50  1.5004 0.130178    
epoca:lugar:bloque   5  14.75    2.95  0.4216 0.829937    
Residual            30 209.92    7.00                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
aov(rdto ~ bloque + epoca * linaje * lugar + Error(bloque %in% lugar + linaje:bloque %in% epoca + bloque %in% lugar:epoca) + bloque, data = data) -> aov.dbca
summary(aov.dbca)

Error: bloque:lugar
          Df Sum Sq Mean Sq F value  Pr(>F)   
bloque     5  174.7    34.9   1.535 0.32488   
lugar      1  580.2   580.2  25.483 0.00394 **
Residuals  5  113.8    22.8                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Error: bloque:linaje:epoca
             Df Sum Sq Mean Sq F value   Pr(>F)    
epoca         1  495.0   495.0  47.152 5.68e-08 ***
linaje        3  149.2    49.7   4.737  0.00708 ** 
epoca:linaje  3   13.5     4.5   0.430  0.73283    
Residuals    35  367.5    10.5                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Error: bloque:lugar:epoca
            Df Sum Sq Mean Sq F value Pr(>F)
epoca:lugar  1   6.00    6.00   2.034  0.213
Residuals    5  14.75    2.95               

Error: Within
                   Df Sum Sq Mean Sq F value  Pr(>F)   
linaje:lugar        3  99.08   33.03   4.720 0.00816 **
epoca:linaje:lugar  3  20.25    6.75   0.965 0.42221   
Residuals          30 209.92    7.00                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
broom::tidy(aov.dbca)
# A tibble: 12 × 7
   stratum             term                  df  sumsq meansq statistic  p.value
   <chr>               <chr>              <dbl>  <dbl>  <dbl>     <dbl>    <dbl>
 1 bloque:lugar        bloque                 5 175.    34.9      1.53   3.25e-1
 2 bloque:lugar        lugar                  1 580.   580.      25.5    3.94e-3
 3 bloque:lugar        Residuals              5 114.    22.8     NA     NA      
 4 bloque:linaje:epoca epoca                  1 495.   495.      47.2    5.68e-8
 5 bloque:linaje:epoca linaje                 3 149.    49.7      4.74   7.08e-3
 6 bloque:linaje:epoca epoca:linaje           3  13.5    4.51     0.430  7.33e-1
 7 bloque:linaje:epoca Residuals             35 367.    10.5     NA     NA      
 8 bloque:lugar:epoca  epoca:lugar            1   6      6        2.03   2.13e-1
 9 bloque:lugar:epoca  Residuals              5  14.7    2.95    NA     NA      
10 Within              linaje:lugar           3  99.1   33.0      4.72   8.16e-3
11 Within              epoca:linaje:lugar     3  20.2    6.75     0.965  4.22e-1
12 Within              Residuals             30 210.     7.00    NA     NA      
broom::tidy(gad(modelo.dbca))
# A tibble: 12 × 6
   term                   df  sumsq meansq statistic       p.value
   <chr>               <int>  <dbl>  <dbl>     <dbl>         <dbl>
 1 epoca                   1 495.   495.      47.2    0.0000000568
 2 linaje                  3 149.    49.7      4.74   0.00708     
 3 lugar                   1 580.   580.      25.5    0.00394     
 4 bloque                  5 175.    34.9      3.33   0.0146      
 5 epoca:linaje            3  13.5    4.51     0.430  0.733       
 6 epoca:lugar             1   6.00   6.00     2.03   0.213       
 7 linaje:lugar            3  99.1   33.0      4.72   0.00816     
 8 lugar:bloque            5 114.    22.8      3.25   0.0183      
 9 epoca:linaje:lugar      3  20.2    6.75     0.965  0.422       
10 epoca:linaje:bloque    35 367.    10.5      1.50   0.130       
11 epoca:lugar:bloque      5  14.7    2.95     0.422  0.830       
12 Residual               30 210.     7.00    NA     NA           

Conclusión.

Con respecto al Factor epoca: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor epoca tienen un efecto sobre el rendimiento estadísticamente diferente a 0.

Con respecto al Factor linaje: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor linaje tienen un efecto sobre el rendimiento estadísticamente diferente a 0.

Con respecto al Factor lugar: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor lugar tienen un efecto sobre el rendimiento estadísticamente diferente a 0.

agricolae::cv.model(modelo.dbca)
[1] 16.90691

Comparaciones de medias para los efectos principales del Factor Lugar

get_df_term <- function(object, name_FA) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  df_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(endsWith(stratum, paste0(":",name_FA)) & 
                    term == "Residuals") %>%
    dplyr::pull(df)
  return(df_rep_A_residuals)
}
get_df_term(aov.dbca, paste0("linaje",":","epoca"))
[1] 35
get_mse_term <- function(object, name_FA) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  meansq_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(endsWith(stratum, paste0(":",name_FA)) & 
                    term == "Residuals") %>%
    dplyr::pull(meansq)
  return(meansq_rep_A_residuals)
}
get_mse_term(aov.dbca, paste0("linaje",":","epoca"))
[1] 10.49881
data %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  epoca, # Cambiar según nombre de variable independiente
  DFerror = get_df_term(aov.dbca, paste0("linaje",":","epoca")), 
  MSerror = get_mse_term(aov.dbca, paste0("linaje",":","epoca")),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ epoca

LSD t Test for rdto 

Mean Square Error:  10.49881 

epoca,  means and individual ( 95 %) CI

      rdto      std  r      LCL      UCL Min Max
1 13.37500 3.895579 48 12.42556 14.32444   4  26
2 17.91667 4.694194 48 16.96722 18.86611   7  27

Alpha: 0.05 ; DF Error: 35
Critical Value of t: 2.030108 

least Significant Difference: 1.342714 

Treatments with the same letter are not significantly different.

      rdto groups
2 17.91667      a
1 13.37500      b

Comparaciones de medias para los efectos principales del Factor Linaje

data %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  linaje, # Cambiar según nombre de variable independiente
  DFerror = get_df_term(aov.dbca, paste0("linaje",":","epoca")), 
  MSerror = get_mse_term(aov.dbca, paste0("linaje",":","epoca")),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ linaje

LSD t Test for rdto 

Mean Square Error:  10.49881 

linaje,  means and individual ( 95 %) CI

      rdto      std  r      LCL      UCL Min Max
1 16.54167 4.736346 24 15.19895 17.88438   9  27
2 16.95833 4.685585 24 15.61562 18.30105  10  26
3 15.33333 4.410133 24 13.99062 16.67605   9  22
4 13.75000 5.219112 24 12.40729 15.09271   4  24

Alpha: 0.05 ; DF Error: 35
Critical Value of t: 2.030108 

least Significant Difference: 1.898884 

Treatments with the same letter are not significantly different.

      rdto groups
2 16.95833      a
1 16.54167      a
3 15.33333     ab
4 13.75000      b

Comparaciones de medias para los efectos principales del Factor Lugar

data %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  lugar, # Cambiar según nombre de variable independiente
  DFerror = get_df_term(aov.dbca, "lugar"), 
  MSerror = get_mse_term(aov.dbca, "lugar"),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ lugar

LSD t Test for rdto 

Mean Square Error:  22.76667 

lugar,  means and individual ( 95 %) CI

          rdto      std  r      LCL      UCL Min Max
Lima  13.18750 3.987514 48 11.41714 14.95786   4  26
Pisco 18.10417 4.415830 48 16.33381 19.87452   9  27

Alpha: 0.05 ; DF Error: 5
Critical Value of t: 2.570582 

least Significant Difference: 2.503661 

Treatments with the same letter are not significantly different.

          rdto groups
Pisco 18.10417      a
Lima  13.18750      b

Comparaciones de medias para las interacciones linaje (B) x lugar (C)

Para los niveles del factor B dentro del nivel C1:

  • B1 vs B2:

\(H_0: \mu_{B1} - \mu_{B2} = 0\)

\(H_1: \mu_{B1} - \mu_{B2} \neq 0\)

  • B1 vs B3:

\(H_0: \mu_{B1} - \mu_{B3} = 0\)

\(H_1: \mu_{B1} - \mu_{B3} \neq 0\)

  • B2 vs B3:

\(H_0: \mu_{B2} - \mu_{B3} = 0\)

\(H_1: \mu_{B2} - \mu_{B3} \neq 0\)

  • B3 vs B4:

\(H_0: \mu_{B3} - \mu_{B4} = 0\)

\(H_1: \mu_{B3} - \mu_{B4} \neq 0\)

Para los niveles del factor B dentro del nivel C1:

  • B1 vs B2:

\(H_0: \mu_{B1} - \mu_{B2} = 0\)

\(H_1: \mu_{B1} - \mu_{B2} \neq 0\)

NOTA: Repetir este proceso para cada nivel de B y cada nivel de C.

emmeans::joint_tests(modelo.dbca, by = c("epoca"))
epoca = 1:
 model term    df1 df2 F.ratio p.value
 linaje          3  30   2.513  0.0774
 lugar           1  30  33.454  <.0001
 bloque          5  30   1.701  0.1649
 linaje:lugar    3  30   0.941  0.4332
 linaje:bloque  15  30   1.601  0.1329
 lugar:bloque    5  30   1.105  0.3784

epoca = 2:
 model term    df1 df2 F.ratio p.value
 linaje          3  30   5.240  0.0050
 lugar           1  30  50.318  <.0001
 bloque          5  30   4.106  0.0058
 linaje:lugar    3  30   4.744  0.0080
 linaje:bloque  15  30   1.629  0.1243
 lugar:bloque    5  30   2.570  0.0475
filter_by_2factor_level <- function(data, factor_name1, factor_name2) {
  levels1 <- levels(data[[deparse(substitute(factor_name1))]])
  filters1 <- purrr::map(levels1, ~ filter(data, {{factor_name1}} == .x))
  names(filters1) <- levels1
  
  levels2 <- levels(data[[deparse(substitute(factor_name2))]])
  filters2 <- purrr::map(levels2, ~ filter(data, {{factor_name2}} == .x))
  names(filters2) <- levels2
  
  result <- list()
  result[[deparse(substitute(factor_name1))]] <- filters1
  result[[deparse(substitute(factor_name2))]] <- filters2
  return(result)
}
datos_filtrados <- filter_by_2factor_level(data = data,
                       factor_name1 = linaje,
                       factor_name2 = lugar)
multcomp.test_2factors <- function(object, respuesta, factor_name1, factor_name2, test, aov){
  
  # Función auxiliar para aplicar la prueba de comparaciones múltiples a un data frame
  multcomp_df <- function(df, respuesta, factor_name, test, aov){
    if (test == "LSD") {
      comp <- LSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "HSD") {
      comp <- HSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "duncan") {
      comp <- duncan.test(df[[respuesta]],
                          df[[factor_name]],
                          DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                          group=TRUE,
                          main = NULL,
                          console=FALSE)[[6]]
    } else if (test == "SNK") {
      comp <- SNK.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[6]]
    } else {
      stop("Test no válido. Los tests disponibles son LSD, HSD, duncan, y SNK.")
    }
    
    return(comp %>%
             rename("y" = "df[[respuesta]]")
           )
  }
  
  # Aplicar la prueba de comparaciones múltiples a todos los data frames dentro de filters1
  comp_filters1 <- lapply(object[[1]], function(df){
    multcomp_df(df, respuesta, factor_name2, test, aov) %>%
      arrange(row.names(.)) %>%
      rownames_to_column(var = "x") %>%
      relocate(x)
  })
  
  # Aplicar la prueba de comparaciones múltiples a todos los data frames dentro de filters2
  comp_filters2 <- lapply(object[[2]], function(df){
    multcomp_df(df, respuesta, factor_name1, test, aov) %>%
      dplyr::arrange(row.names(.)) %>%
      rownames_to_column(var = "x") %>%
      relocate(x) %>%
      dplyr::mutate(groups = toupper(groups))
  })
  
  row.names(comp_filters1) <- NULL
  row.names(comp_filters2) <- NULL
  # Retornar una lista con las comparaciones múltiples para cada data frame
  result <- list()
  result[[as.name(substitute(factor_name1))]] <- comp_filters1
  result[[as.name(substitute(factor_name2))]] <- comp_filters2
  return(#list(#"Comparación de los niveles del factor B dentro de cada nivel del factor A",
         result#[[1]],
         # "Comparación de los niveles del factor A dentro de cada nivel del factor B",
         # result[[2]]
         # )
  )
}
multcomp.test_2factors(
  object = datos_filtrados,
  respuesta = "rdto",
  factor_name1 = "linaje",
  factor_name2 = "lugar",
  test = "duncan",
  aov = modelo.dbca) -> result.comp
result.comp
$linaje
$linaje$`1`
      x        y groups
1  Lima 15.58333      a
2 Pisco 17.50000      a

$linaje$`2`
      x        y groups
1  Lima 14.83333      b
2 Pisco 19.08333      a

$linaje$`3`
      x        y groups
1  Lima 12.16667      b
2 Pisco 18.50000      a

$linaje$`4`
      x        y groups
1  Lima 10.16667      b
2 Pisco 17.33333      a


$lugar
$lugar$Lima
  x        y groups
1 1 15.58333      A
2 2 14.83333      A
3 3 12.16667      B
4 4 10.16667      B

$lugar$Pisco
  x        y groups
1 1 17.50000      A
2 2 19.08333      A
3 3 18.50000      A
4 4 17.33333      A
# Convertir la lista a un data frame
df <- result.comp %>%
  reshape2::melt() %>% 
  ungroup() %>%
  dplyr::select(-variable) %>%
  relocate("Factor" = "L1",
           "Nivel" = "L2",
           x,
           "y" = "value",
           groups)
df
   Factor Nivel     x        y groups
1  linaje     1  Lima 15.58333      a
2  linaje     1 Pisco 17.50000      a
3  linaje     2  Lima 14.83333      b
4  linaje     2 Pisco 19.08333      a
5  linaje     3  Lima 12.16667      b
6  linaje     3 Pisco 18.50000      a
7  linaje     4  Lima 10.16667      b
8  linaje     4 Pisco 17.33333      a
9   lugar  Lima     1 15.58333      A
10  lugar  Lima     2 14.83333      A
11  lugar  Lima     3 12.16667      B
12  lugar  Lima     4 10.16667      B
13  lugar Pisco     1 17.50000      A
14  lugar Pisco     2 19.08333      A
15  lugar Pisco     3 18.50000      A
16  lugar Pisco     4 17.33333      A
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # # Convertir level1 y level2 en nombres simbólicos
  # level1 <- as.name(level1)
  # level2 <- as.name(level2)
  # 
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1, level2)) %>%
    dplyr::mutate(groups = paste0(groups.y,groups.x)) %>%
    dplyr::select(!!level1,!!level2, y, groups) #%>%
    # rename(!!level1 := x,
    #        !!level2 := Nivel)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
df2 <- create_report(df = df,
               level1 = "linaje",
               level2 = "lugar") 
df2 %>% gt()
linaje lugar y groups
1 Lima 15.58333 Aa
1 Pisco 17.50000 Aa
2 Lima 14.83333 Ab
2 Pisco 19.08333 Aa
3 Lima 12.16667 Bb
3 Pisco 18.50000 Aa
4 Lima 10.16667 Bb
4 Pisco 17.33333 Aa
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1,level2)) %>%
    dplyr::mutate(y = paste0(round(y,2), " ", groups.y, groups.x)) %>%
    dplyr::select(!!level1,!!level2, y)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
df3 <- create_report(df = df,
               level1 = "linaje",
               level2 = "lugar") 
df3 %>% gt()
linaje lugar y
1 Lima 15.58 Aa
1 Pisco 17.5 Aa
2 Lima 14.83 Ab
2 Pisco 19.08 Aa
3 Lima 12.17 Bb
3 Pisco 18.5 Aa
4 Lima 10.17 Bb
4 Pisco 17.33 Aa
df3 %>% 
 pivot_wider(names_from = lugar,
             values_from = c(y), 
             names_glue = "{lugar}") %>%
  gt()
linaje Lima Pisco
1 15.58 Aa 17.5 Aa
2 14.83 Ab 19.08 Aa
3 12.17 Bb 18.5 Aa
4 10.17 Bb 17.33 Aa

Experimentos con medidas repetidas


Análisis de DCA con medidas repetidas


Importación de datos


archivos <- list.files(pattern = "datos exp. repetidos.xlsx", 
                       full.names = TRUE,
                       recursive = TRUE)

# Importación
data <- readxl::read_xlsx(archivos,
                           sheet = "tiempo")

# Preprocesamiento

data <- data %>%
  pivot_longer(cols = starts_with("s"),
               names_to = "tiempo",
               values_to = "y") %>%
  mutate_if(is.character, factor) %>%
  mutate(rep = as.factor(rep),
         tiempo = factor(tiempo,
                         levels = c(
                           "s3","s4","s10","s12","s15", "s16")))

Definición del modelo


modelo.dca <- lm(y ~ variedad*tiempo + rep:variedad, data = data)

Nota

  • La expresión “rep:variedad” es para considerar la interacción como efecto aleatorio.
  • La expresión “rep %in% variedad” permite que se genere una estructura del análisis de varianza donde se anide el efecto de la variedad dentro de cada bloque
summary(modelo.dca)

Call:
lm(formula = y ~ variedad * tiempo + rep:variedad, data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-67.167  -3.917   0.278   3.208  69.333 

Coefficients:
                             Estimate Std. Error t value Pr(>|t|)    
(Intercept)                   -1.7778    15.5591  -0.114 0.909413    
variedadDuraznillo            15.6111    22.0039   0.709 0.480780    
variedadNegra                 21.7778    22.0039   0.990 0.326283    
variedadPukaÑawi              -2.3889    22.0039  -0.109 0.913908    
variedadTumbay                18.8889    22.0039   0.858 0.394068    
variedadYanaPepino            13.4444    22.0039   0.611 0.543505    
tiempos4                      -9.6667    19.0559  -0.507 0.613818    
tiempos10                     81.3333    19.0559   4.268 7.12e-05 ***
tiempos12                     81.0000    19.0559   4.251 7.56e-05 ***
tiempos15                    -12.6667    19.0559  -0.665 0.508782    
tiempos16                    -15.3333    19.0559  -0.805 0.424198    
variedadDuraznillo:tiempos4    1.6667    26.9491   0.062 0.950892    
variedadNegra:tiempos4         2.3333    26.9491   0.087 0.931291    
variedadPukaÑawi:tiempos4      1.3333    26.9491   0.049 0.960704    
variedadTumbay:tiempos4        6.3333    26.9491   0.235 0.815001    
variedadYanaPepino:tiempos4    4.3333    26.9491   0.161 0.872794    
variedadDuraznillo:tiempos10 -96.3333    26.9491  -3.575 0.000700 ***
variedadNegra:tiempos10      -93.6667    26.9491  -3.476 0.000953 ***
variedadPukaÑawi:tiempos10    -5.0000    26.9491  -0.186 0.853435    
variedadTumbay:tiempos10     -87.6667    26.9491  -3.253 0.001877 ** 
variedadYanaPepino:tiempos10 -92.6667    26.9491  -3.439 0.001069 ** 
variedadDuraznillo:tiempos12 -63.6667    26.9491  -2.362 0.021414 *  
variedadNegra:tiempos12      -79.6667    26.9491  -2.956 0.004447 ** 
variedadPukaÑawi:tiempos12   -36.6667    26.9491  -1.361 0.178733    
variedadTumbay:tiempos12     -85.6667    26.9491  -3.179 0.002339 ** 
variedadYanaPepino:tiempos12 -77.0000    26.9491  -2.857 0.005865 ** 
variedadDuraznillo:tiempos15  -5.3333    26.9491  -0.198 0.843789    
variedadNegra:tiempos15       -5.0000    26.9491  -0.186 0.853435    
variedadPukaÑawi:tiempos15    -4.3333    26.9491  -0.161 0.872794    
variedadTumbay:tiempos15      -5.0000    26.9491  -0.186 0.853435    
variedadYanaPepino:tiempos15  -2.0000    26.9491  -0.074 0.941087    
variedadDuraznillo:tiempos16  -4.0000    26.9491  -0.148 0.882503    
variedadNegra:tiempos16       -4.6667    26.9491  -0.173 0.863104    
variedadPukaÑawi:tiempos16    -3.0000    26.9491  -0.111 0.911733    
variedadTumbay:tiempos16      -3.3333    26.9491  -0.124 0.901974    
variedadYanaPepino:tiempos16   0.6667    26.9491   0.025 0.980346    
variedadCanchan:rep2          11.5000    13.4746   0.853 0.396798    
variedadDuraznillo:rep2        3.0000    13.4746   0.223 0.824570    
variedadNegra:rep2             1.3333    13.4746   0.099 0.921506    
variedadPukaÑawi:rep2         47.5000    13.4746   3.525 0.000817 ***
variedadTumbay:rep2            2.1667    13.4746   0.161 0.872794    
variedadYanaPepino:rep2        0.1667    13.4746   0.012 0.990172    
variedadCanchan:rep3          40.8333    13.4746   3.030 0.003601 ** 
variedadDuraznillo:rep3       13.5000    13.4746   1.002 0.320421    
variedadNegra:rep3            -1.3333    13.4746  -0.099 0.921506    
variedadPukaÑawi:rep3         21.0000    13.4746   1.558 0.124376    
variedadTumbay:rep3            5.5000    13.4746   0.408 0.684597    
variedadYanaPepino:rep3        8.8333    13.4746   0.656 0.514615    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 23.34 on 60 degrees of freedom
Multiple R-squared:  0.7304,    Adjusted R-squared:  0.5193 
F-statistic: 3.459 on 47 and 60 DF,  p-value: 3.949e-06

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dca)
ggResidpanel::resid_panel(modelo.dca)
influence.measures(modelo.dca)
Influence measures of
     lm(formula = y ~ variedad * tiempo + rep:variedad, data = data) :

       dfb.1_  dfb.vrdD  dfb.vrdN  dfb.vrPÑ  dfb.vrdT  dfb.vrYP  dfb.tmp4
1    9.14e-01 -6.47e-01 -6.47e-01 -6.47e-01 -6.47e-01 -6.47e-01 -5.60e-01
2    2.90e-01 -2.05e-01 -2.05e-01 -2.05e-01 -2.05e-01 -2.05e-01  7.11e-01
3   -6.17e-01  4.36e-01  4.36e-01  4.36e-01  4.36e-01  4.36e-01 -1.95e-16
4   -3.41e-01  2.41e-01  2.41e-01  2.41e-01  2.41e-01  2.41e-01 -3.99e-15
5    1.85e-01 -1.31e-01 -1.31e-01 -1.31e-01 -1.31e-01 -1.31e-01 -2.05e-16
6    2.20e-01 -1.55e-01 -1.55e-01 -1.55e-01 -1.55e-01 -1.55e-01  6.83e-16
7    7.26e-02 -5.13e-02 -5.13e-02 -5.13e-02 -5.13e-02 -5.13e-02 -7.11e-02
8   -1.88e-02  1.33e-02  1.33e-02  1.33e-02  1.33e-02  1.33e-02  9.20e-02
9    7.71e-02 -5.45e-02 -5.45e-02 -5.45e-02 -5.45e-02 -5.45e-02  4.06e-16
10   1.10e-02 -7.76e-03 -7.76e-03 -7.76e-03 -7.76e-03 -7.76e-03  9.24e-17
11  -1.88e-02  1.33e-02  1.33e-02  1.33e-02  1.33e-02  1.33e-02 -1.42e-16
12  -3.58e-02  2.53e-02  2.53e-02  2.53e-02  2.53e-02  2.53e-02 -7.05e-16
13  -6.46e-01  4.57e-01  4.57e-01  4.57e-01  4.57e-01  4.57e-01  6.33e-01
14   1.65e-01 -1.17e-01 -1.17e-01 -1.17e-01 -1.17e-01 -1.17e-01 -8.07e-01
15  -4.06e-01  2.87e-01  2.87e-01  2.87e-01  2.87e-01  2.87e-01  9.41e-16
16  -1.82e-01  1.29e-01  1.29e-01  1.29e-01  1.29e-01  1.29e-01 -5.43e-15
17   1.12e-01 -7.90e-02 -7.90e-02 -7.90e-02 -7.90e-02 -7.90e-02 -5.10e-16
18   1.47e-01 -1.04e-01 -1.04e-01 -1.04e-01 -1.04e-01 -1.04e-01  1.61e-17
19   3.32e-17 -6.19e-17  1.33e-18  8.62e-17 -5.55e-17  1.92e-01 -2.02e-16
20   9.74e-17 -9.51e-17 -4.84e-17 -4.78e-17 -1.50e-16  3.31e-02 -1.27e-16
21   4.03e-19  2.55e-18 -1.50e-19 -2.04e-19  0.00e+00 -3.00e-03 -1.44e-18
22   9.06e-16 -1.03e-15 -7.74e-16 -6.10e-16 -7.19e-16 -1.33e-01 -8.29e-16
23   1.73e-17 -3.48e-17 -1.13e-17 -1.37e-17 -1.37e-17  2.70e-02 -2.51e-18
24  -7.10e-17  2.28e-17  6.06e-17  7.16e-17  6.05e-17  2.70e-02  4.89e-17
25   7.14e-17 -4.51e-17 -3.95e-17 -1.06e-16 -6.91e-17 -4.13e-02 -1.01e-17
26  -1.14e-18  2.52e-18 -6.89e-19  8.94e-19  4.06e-18 -2.25e-03 -1.24e-18
27   1.06e-17 -1.04e-17 -7.47e-18 -6.17e-18 -4.71e-18  2.25e-03 -9.59e-18
28  -1.61e-16  1.40e-16  1.07e-16  1.40e-16  1.51e-16  1.73e-02  8.24e-17
29   1.67e-17 -1.60e-17 -1.55e-17 -5.22e-17 -1.84e-17 -1.28e-02  9.17e-18
30   9.57e-18  1.97e-17 -9.41e-18 -2.06e-18 -3.22e-17 -1.28e-02  1.09e-17
31  -2.10e-17  2.98e-17  7.25e-18 -6.64e-17  4.55e-17 -7.89e-02  1.06e-16
32   3.22e-17 -3.35e-17 -3.05e-17  7.28e-18 -2.03e-17  1.88e-02 -2.96e-18
33  -1.61e-19  2.89e-20  1.91e-18 -6.40e-18 -8.12e-19 -3.76e-03  6.32e-18
34   8.25e-16 -7.37e-16 -4.79e-16 -6.14e-16 -5.04e-16 -8.42e-02 -1.92e-16
35   1.17e-16 -7.39e-17 -8.72e-17 -4.29e-17 -9.11e-17  2.63e-02 -1.47e-16
36   4.34e-17 -6.58e-17 -4.82e-17 -4.54e-17 -1.90e-18  2.63e-02 -3.88e-17
37  -7.39e-16  3.57e-16  6.61e-16  7.73e-01  2.57e-16  3.46e-16 -2.87e-16
38  -9.97e-17  1.00e-16  8.00e-17  1.87e-01 -1.10e-17  1.60e-16  2.11e-16
39   2.30e-16 -6.39e-17 -2.07e-16 -6.98e-01  1.84e-16  7.72e-17 -4.50e-16
40  -1.14e-17  6.11e-17 -1.05e-16 -2.12e-01  2.10e-17 -1.42e-16  6.83e-17
41  -1.58e-16  5.02e-17  1.35e-16  2.40e-01  6.70e-17  2.00e-16  1.74e-16
42  -2.16e-16  1.25e-16  1.96e-16  2.06e-01 -5.32e-18  1.23e-16  3.67e-16
43   1.86e-16 -3.94e-17 -1.97e-16 -5.34e-01  1.22e-16  5.62e-17  2.80e-16
44   1.70e-16 -8.45e-17 -9.90e-17  9.11e-02 -8.77e-17 -2.04e-16 -3.05e-16
45   3.38e-17 -1.53e-18 -7.65e-18 -1.16e-01 -5.31e-17 -5.60e-17  1.41e-16
46   3.84e-16 -3.17e-16  0.00e+00 -3.64e-01 -1.43e-16  1.07e-15 -8.77e-17
47  -8.65e-17  5.33e-17  5.18e-17  1.21e-01 -9.08e-17 -1.71e-16 -1.94e-16
48   1.19e-16 -1.29e-16 -1.09e-16  1.15e-01 -1.27e-17 -1.27e-16 -4.02e-16
49  -2.28e-17  8.12e-18  1.54e-17  4.88e-02 -7.66e-18 -1.05e-18 -2.60e-17
50   3.76e-18 -2.41e-18 -1.85e-18  2.25e-03 -1.59e-18 -3.38e-18 -6.56e-18
51   1.06e-16 -3.35e-17 -7.18e-17 -1.98e-01 -1.56e-16 -1.82e-16  2.33e-16
52  -2.79e-16  2.15e-16  7.29e-17  2.21e-01  1.62e-16 -4.05e-16  5.06e-17
53   6.18e-19 -3.70e-19 -5.19e-19 -7.51e-04  1.58e-19  1.00e-18  1.18e-18
54  -9.97e-18  1.33e-17  6.31e-18 -1.13e-02 -1.64e-18  4.18e-18  3.77e-17
55   4.56e-16  1.86e-01 -2.05e-16 -2.06e-16 -1.94e-16 -1.76e-16  1.32e-15
56   4.81e-16  1.01e-01 -2.85e-16 -2.93e-16 -3.21e-16 -2.97e-16  6.55e-16
57   3.85e-17  1.95e-02 -1.83e-17 -1.67e-17 -1.90e-17 -2.17e-17  1.35e-16
58  -7.94e-16 -2.60e-01  3.41e-16  4.12e-16  4.06e-16  3.92e-16 -1.68e-15
59   1.15e-16  3.76e-02 -5.29e-17 -5.60e-17 -4.94e-17 -6.19e-17  2.39e-16
60   1.28e-16  4.96e-02 -5.12e-17 -7.76e-17 -7.26e-17 -7.42e-17  3.27e-16
61   1.67e-16  7.14e-02 -7.13e-17 -6.70e-17 -6.45e-17 -5.75e-17  4.30e-16
62   1.12e-18  8.26e-03  1.35e-17  1.03e-17  1.91e-17  1.66e-17  1.04e-16
63  -6.41e-17 -1.43e-02  3.06e-17  3.62e-17  2.99e-17  2.73e-17 -1.84e-16
64   9.40e-17  3.69e-02 -4.60e-17 -3.95e-17 -2.86e-17 -3.18e-17  4.94e-16
65  -1.27e-17 -5.26e-03  5.56e-18  5.99e-18  6.67e-18  2.33e-18 -7.21e-17
66  -3.33e-17 -1.13e-02  2.04e-17  1.09e-17  1.10e-17  3.28e-19 -1.49e-16
67  -4.20e-16 -1.88e-01  1.75e-16  1.67e-16  1.55e-16  1.28e-16 -1.11e-15
68   1.43e-17  4.22e-02  6.29e-17  5.93e-17  8.99e-17  6.98e-17  5.60e-16
69   1.17e-16  2.41e-02 -5.50e-17 -6.28e-17 -5.46e-17 -4.99e-17  3.20e-16
70  -5.09e-16 -1.70e-01  2.61e-16  1.96e-16  1.86e-16  2.41e-16 -2.37e-15
71   7.11e-17  2.41e-02 -3.23e-17 -3.40e-17 -3.82e-17 -2.14e-17  3.38e-16
72   1.28e-16  3.61e-02 -7.57e-17 -4.57e-17 -4.66e-17 -3.14e-17  4.96e-16
73   6.59e-17 -4.91e-17 -7.98e-17 -2.32e-17  6.81e-02 -3.69e-17  1.15e-17
74   2.08e-17 -1.84e-17 -2.01e-17 -1.50e-17  1.10e-02 -1.51e-17 -4.34e-18
75  -1.16e-17  1.11e-17  1.19e-17  7.63e-18 -1.60e-02  1.01e-17 -1.73e-17
76  -8.43e-17  6.21e-17  6.10e-17  4.34e-17 -4.91e-02  5.31e-17 -2.03e-17
77   4.83e-17 -3.48e-17 -4.08e-17 -3.29e-17  2.30e-02 -2.94e-17  4.86e-19
78   3.20e-17 -2.42e-17 -2.79e-17 -2.29e-17  1.40e-02 -9.54e-18 -4.47e-18
79   1.33e-17 -1.06e-17 -1.80e-17 -3.54e-18  1.63e-02 -8.28e-18  5.01e-18
80   5.53e-18 -1.05e-17 -6.00e-20 -7.56e-18 -9.26e-03 -7.80e-18 -1.59e-17
81   1.66e-17 -8.90e-18 -1.84e-17 -7.75e-18  8.76e-03 -3.36e-18 -1.49e-17
82   5.87e-19 -4.70e-19  1.95e-18 -1.19e-18 -1.75e-03 -6.51e-19  6.97e-19
83  -3.17e-18  3.14e-18  1.08e-19  2.25e-18  2.75e-03  3.00e-18  9.30e-19
84  -2.25e-18  2.58e-18  1.32e-19  5.24e-18  2.75e-03 -3.25e-19  1.82e-18
85  -5.28e-17  4.30e-17  6.68e-17  1.92e-17 -5.88e-02  3.34e-17 -1.07e-17
86  -1.44e-17  1.97e-17  4.03e-18  1.81e-17  1.48e-02  1.62e-17  3.46e-17
87  -2.68e-17  1.56e-17  3.24e-17  1.03e-17 -1.68e-02  3.88e-18  2.81e-17
88   1.38e-17 -1.06e-17  1.82e-17 -2.33e-17 -2.28e-02 -1.19e-17  1.01e-17
89  -1.02e-17  9.51e-18  1.11e-18  1.25e-17  8.76e-03  8.66e-18  1.02e-18
90  -2.48e-18  3.68e-18  2.72e-19  7.81e-18  4.26e-03 -1.18e-18  2.37e-18
91   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
92  -1.26e-17  5.82e-18  3.01e-02  7.27e-18  5.02e-18  1.30e-17  4.49e-17
93   2.54e-18  3.10e-18 -2.40e-02  8.18e-19 -4.88e-18 -9.10e-18 -8.49e-18
94  -4.09e-17  4.19e-17 -4.81e-02  2.61e-17  1.79e-17  1.55e-17  4.22e-18
95   5.42e-18 -1.09e-17  4.21e-02 -2.53e-18 -4.07e-18 -1.76e-18  1.55e-17
96   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
97  -2.63e-17  1.78e-17 -3.00e-02  1.41e-17  1.24e-17  1.79e-17  2.74e-17
98   1.11e-17 -5.52e-18  9.01e-03 -5.45e-18 -5.85e-18 -1.19e-17 -3.60e-17
99  -6.39e-18  3.05e-18 -4.51e-03  1.15e-18  3.90e-18  6.23e-18  6.13e-18
100  1.66e-18 -2.13e-17 -3.31e-02 -1.96e-17 -9.38e-18 -9.42e-18  1.66e-17
101  3.68e-18  5.86e-18  1.65e-02 -9.51e-19 -2.02e-18 -8.30e-18 -2.21e-17
102  4.79e-18 -3.88e-18  6.01e-03 -1.81e-18 -3.68e-21 -4.60e-18 -7.52e-18
103  2.39e-17 -1.47e-17  3.00e-02 -1.19e-17 -1.15e-17 -1.69e-17 -2.76e-17
104  9.25e-18 -5.43e-18  6.01e-03 -5.07e-18 -4.85e-18 -8.91e-18 -2.25e-17
105 -1.09e-17  6.30e-18 -7.51e-03  2.19e-18  6.60e-18  9.26e-18  1.00e-17
106 -6.20e-19  5.23e-18  9.01e-03  6.54e-18  2.44e-18  1.51e-18 -3.15e-18
107  3.06e-18  0.00e+00  4.51e-03 -1.08e-18 -1.26e-18 -2.41e-18 -6.13e-18
108 -5.79e-18  4.65e-18 -6.01e-03  2.31e-18  9.47e-19  4.43e-18  7.18e-18
     dfb.tm10  dfb.tm12  dfb.tm15  dfb.tm16  dfb.vD.4  dfb.vN.4 dfb.vPÑ.4
1   -5.60e-01 -5.60e-01 -5.60e-01 -5.60e-01  3.96e-01  3.96e-01  3.96e-01
2   -1.13e-14 -1.12e-14 -1.17e-14 -1.18e-14 -5.03e-01 -5.03e-01 -5.03e-01
3   -1.51e+00 -2.19e-15 -2.14e-15 -2.50e-15  1.83e-15 -4.77e-16 -7.30e-16
4   -5.93e-15 -8.35e-01 -4.95e-15 -5.65e-15  3.36e-15  2.48e-15  5.13e-15
5    4.03e-16 -6.17e-17  4.54e-01  3.40e-16 -3.96e-16  1.29e-16  1.46e-16
6    1.34e-15  9.68e-16  4.14e-16  5.39e-01 -1.16e-15 -4.08e-16  3.59e-17
7   -7.11e-02 -7.11e-02 -7.11e-02 -7.11e-02  5.03e-02  5.03e-02  5.03e-02
8    7.92e-16  7.26e-16  6.79e-16  8.65e-16 -6.50e-02 -6.50e-02 -6.50e-02
9   -3.78e-01  1.29e-15  1.16e-15  8.20e-16 -4.77e-16 -9.29e-17 -2.02e-16
10   9.20e-17 -5.38e-02  8.72e-18  1.12e-16 -7.54e-17 -3.52e-17 -1.05e-16
11  -1.58e-16 -2.75e-16  9.20e-02 -1.98e-16  9.90e-17  9.17e-17  4.75e-17
12  -3.65e-16 -7.54e-16 -5.23e-16  1.75e-01  6.73e-16  5.00e-16  4.54e-16
13   6.33e-01  6.33e-01  6.33e-01  6.33e-01 -4.48e-01 -4.48e-01 -4.48e-01
14  -3.39e-15 -2.14e-15 -3.07e-15 -2.38e-15  5.71e-01  5.71e-01  5.71e-01
15   1.99e+00 -7.37e-17  2.03e-15  1.51e-15  4.03e-16 -9.78e-16 -3.79e-16
16  -4.54e-15  8.92e-01 -6.82e-15 -5.86e-15  4.68e-15  3.87e-15  5.27e-15
17  -8.21e-16  2.73e-16 -5.48e-01 -9.69e-16  3.15e-17  4.20e-16  7.17e-16
18  -1.29e-15  9.76e-16 -6.92e-16 -7.20e-01 -5.46e-16  3.30e-16  1.99e-17
19   1.09e-16 -5.10e-16 -1.90e-16 -2.98e-16  1.68e-16  1.27e-16  2.03e-16
20  -1.29e-16 -1.74e-16 -1.09e-16 -1.03e-16  1.07e-16  8.51e-17  9.19e-17
21   6.73e-19  7.53e-18  4.34e-18 -1.23e-18 -4.52e-19  5.65e-19 -1.30e-18
22  -4.94e-16 -9.38e-16 -7.78e-16 -7.23e-16  9.55e-16  6.48e-16  4.85e-16
23  -2.56e-17 -1.05e-16  2.44e-17 -9.40e-17  1.54e-17  6.22e-18  2.65e-17
24  -3.38e-19  1.99e-17  7.25e-17  2.51e-17 -2.00e-17 -3.83e-17 -3.82e-17
25  -7.99e-17  2.69e-17 -4.88e-17 -4.03e-17  2.92e-18 -3.42e-18  2.43e-17
26   3.04e-18  1.15e-17  1.23e-17  5.88e-18 -7.07e-19  1.69e-18 -2.92e-18
27  -2.91e-18 -1.17e-17 -1.48e-17 -1.11e-17  9.72e-18  6.73e-18  7.48e-18
28   1.76e-16  1.85e-16  9.38e-17  1.15e-16 -7.57e-17 -5.45e-17 -5.58e-17
29  -1.95e-17  1.95e-17 -9.08e-17  5.93e-17 -5.27e-18 -1.30e-18  1.84e-17
30  -4.36e-17  4.59e-17  1.69e-17  1.71e-17 -3.30e-17 -5.62e-18 -2.11e-17
31  -3.98e-17  2.06e-16  6.28e-17  1.14e-16 -7.78e-17 -6.43e-17 -6.75e-17
32  -2.84e-17 -1.07e-16 -3.83e-17 -3.82e-17  2.14e-17  8.86e-18 -1.98e-18
33  -1.70e-18  1.12e-17  4.98e-18 -2.35e-18 -5.16e-18 -5.16e-18 -1.64e-18
34  -5.95e-16 -6.69e-16 -1.70e-16 -3.55e-16  2.49e-16  4.76e-17  1.26e-16
35  -1.05e-16 -1.91e-16 -2.44e-16 -3.22e-17  9.93e-17  1.06e-16  9.26e-17
36   5.46e-17 -1.32e-16 -1.12e-17 -6.06e-17  5.99e-17  3.67e-17  5.30e-17
37   2.11e-16 -2.04e-15 -1.69e-16 -6.67e-17  2.00e-16  1.81e-16 -4.73e-01
38  -5.30e-17 -2.57e-16 -7.37e-17 -7.85e-17 -1.35e-16 -1.48e-16  4.58e-01
39  -2.77e-16  1.06e-15  3.72e-16  7.60e-16  4.21e-16  2.71e-16  3.73e-16
40   2.62e-16  4.44e-16  8.27e-17  2.04e-17 -7.79e-17  1.42e-17 -2.02e-17
41  -2.98e-16 -4.40e-16 -2.09e-16 -4.34e-16 -1.19e-16 -9.62e-17 -5.95e-17
42  -5.62e-17 -2.12e-16 -5.05e-17  8.54e-17 -3.15e-16 -2.89e-16 -4.14e-16
43  -2.89e-16  1.27e-15  3.80e-17 -5.38e-17 -1.88e-16 -1.85e-16  5.23e-01
44  -2.23e-17 -6.11e-16 -3.58e-17 -4.06e-17  2.07e-16  1.97e-16 -4.47e-01
45   1.25e-16  7.46e-16  1.35e-17 -1.03e-16 -1.44e-16 -9.59e-17 -9.37e-17
46  -4.82e-16  2.14e-15  1.46e-16  3.99e-16  1.36e-16 -1.43e-16 -6.41e-17
47   1.90e-16 -7.04e-16  8.00e-17  2.82e-16  1.44e-16  1.30e-16  8.24e-17
48  -2.39e-17 -8.31e-16 -5.33e-17 -1.99e-16  3.66e-16  3.21e-16  4.32e-16
49   2.53e-17 -1.19e-16 -6.93e-18  4.83e-18  1.50e-17  1.97e-17 -4.78e-02
50  -3.59e-19 -1.26e-17 -2.38e-20 -5.00e-19  4.22e-18  3.57e-18 -1.10e-02
51   3.34e-16  1.06e-15 -5.27e-17 -2.21e-16 -2.47e-16 -1.40e-16 -1.82e-16
52   3.07e-16 -1.12e-15 -4.25e-18 -1.93e-16 -6.67e-17  8.10e-17  1.30e-16
53  -1.17e-18  3.65e-18 -5.87e-19 -1.92e-18 -8.92e-19 -7.61e-19 -5.84e-19
54  -7.56e-19  6.82e-17 -2.15e-19  1.41e-17 -3.61e-17 -2.98e-17 -4.16e-17
55   1.61e-16  1.35e-16  1.30e-16  1.36e-16 -1.14e-01 -9.52e-16 -9.74e-16
56   1.57e-17  1.05e-17  1.81e-17 -1.91e-16  2.47e-01 -4.12e-16 -4.60e-16
57   1.57e-17  1.76e-17  1.44e-17  1.90e-17 -9.82e-17 -9.10e-17 -9.74e-17
58  -8.45e-19 -7.69e-17 -2.56e-16 -2.80e-16  1.40e-15  1.20e-15  1.25e-15
59   1.68e-17  2.70e-17  2.33e-17  2.15e-17 -1.74e-16 -1.66e-16 -1.81e-16
60   1.62e-17  3.72e-17  5.47e-17  5.72e-17 -2.23e-16 -2.33e-16 -2.34e-16
61   6.80e-17  4.07e-17  3.59e-17  4.77e-17 -6.99e-02 -3.18e-16 -3.31e-16
62   1.69e-17  1.93e-17  2.10e-17  5.23e-17 -4.05e-02 -8.60e-17 -7.86e-17
63  -1.85e-17 -1.07e-17 -2.03e-17 -8.50e-18  1.41e-16  1.32e-16  1.24e-16
64   8.55e-17  7.39e-17  3.39e-17  1.41e-17 -3.03e-16 -3.45e-16 -3.32e-16
65  -8.32e-18 -7.59e-18 -8.92e-18 -7.33e-18  5.36e-17  5.10e-17  4.74e-17
66  -2.13e-17 -1.54e-17 -1.11e-17 -4.33e-18  1.09e-16  1.03e-16  1.04e-16
67  -1.72e-16 -1.02e-16 -9.47e-17 -1.26e-16  1.84e-01  8.27e-16  8.59e-16
68   8.63e-17  1.06e-16  1.09e-16  2.71e-16 -2.07e-01 -4.52e-16 -4.16e-16
69   2.95e-17  2.23e-17  3.55e-17  1.65e-17 -2.44e-16 -2.30e-16 -2.17e-16
70  -3.82e-16 -3.75e-16 -1.66e-16 -7.99e-17  1.46e-15  1.64e-15  1.59e-15
71   3.50e-17  3.56e-17  3.39e-17  3.57e-17 -2.45e-16 -2.41e-16 -2.25e-16
72   6.67e-17  5.38e-17  3.88e-17  1.39e-17 -3.66e-16 -3.43e-16 -3.45e-16
73   6.51e-17 -2.34e-17  5.91e-17  1.69e-17 -2.11e-18 -1.35e-18 -1.52e-17
74   4.28e-18 -6.17e-19  1.02e-17  2.38e-18  5.64e-18  4.43e-18  8.20e-18
75  -2.81e-17 -1.39e-17 -2.88e-17  3.41e-18  1.76e-17  1.56e-17  1.16e-17
76  -1.32e-17  2.75e-17 -8.38e-17 -1.41e-18  2.79e-17  3.08e-17  2.27e-17
77   6.57e-18 -1.69e-18  3.29e-17 -1.54e-18 -2.18e-18 -4.91e-18 -1.53e-18
78  -2.74e-18 -3.04e-18  1.66e-17 -2.94e-18  2.33e-18  3.71e-18  5.13e-18
79   1.92e-17 -5.74e-18  1.08e-17  6.23e-18 -1.34e-18 -5.00e-19 -3.88e-18
80  -1.63e-17  2.93e-18 -2.16e-17  2.89e-19  2.34e-17  1.62e-17  2.21e-17
81  -6.57e-19 -1.90e-17  5.11e-18  7.24e-18  1.60e-17  1.25e-17  8.81e-18
82  -3.90e-18 -2.69e-18 -1.35e-18 -6.01e-19 -1.33e-18 -1.58e-18 -8.45e-19
83   5.66e-18 -6.80e-19  5.94e-18  1.47e-18 -2.35e-19 -1.06e-19 -6.67e-19
84   7.41e-18 -4.86e-19  4.51e-18  1.34e-18 -1.08e-18 -1.77e-18 -2.83e-18
85  -6.17e-17  2.76e-17 -4.24e-17 -2.17e-17 -2.50e-19  5.57e-20  7.01e-18
86   2.65e-17 -5.74e-18  2.73e-17  1.13e-18 -3.84e-17 -2.70e-17 -3.96e-17
87  -1.24e-18  3.76e-17 -1.77e-18 -1.57e-17 -3.08e-17 -2.31e-17 -1.64e-17
88  -5.07e-17 -3.50e-17 -6.72e-18 -1.03e-17 -1.96e-17 -2.24e-17 -1.29e-17
89   1.76e-17 -4.92e-18  1.17e-17  5.62e-18 -9.00e-20  3.92e-19 -2.65e-18
90   1.14e-17 -1.60e-18  4.32e-18  2.36e-18 -1.55e-18 -2.40e-18 -4.12e-18
91   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
92  -7.29e-18  8.15e-18  1.65e-17 -5.95e-19 -3.40e-17  7.36e-02 -2.07e-17
93  -3.67e-18 -2.71e-18  2.84e-18  7.12e-18  9.57e-18  3.62e-18 -5.31e-18
94   2.08e-17  2.22e-17  1.34e-17  1.89e-17 -1.59e-17 -6.81e-18 -1.04e-17
95  -1.30e-17  8.07e-18  1.74e-18  8.19e-18 -7.88e-18 -1.47e-17 -7.75e-18
96   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
97   1.83e-17  2.24e-17  1.50e-17  1.25e-17 -2.04e-17  2.94e-02 -1.05e-17
98  -1.15e-17 -9.51e-18 -1.53e-17 -6.17e-18  2.55e-17 -4.42e-02  1.59e-17
99   1.10e-17  3.33e-18  1.63e-18  5.94e-19 -5.93e-18 -4.57e-18  2.63e-19
100  3.55e-17  1.54e-17  1.37e-18 -2.06e-18 -4.73e-19 -2.96e-17  1.63e-18
101 -1.82e-17 -1.65e-17 -7.97e-18 -1.84e-17  1.29e-17  2.68e-17  1.24e-17
102 -2.77e-18 -1.73e-18 -7.83e-18 -1.03e-18  9.05e-18  9.66e-18  4.58e-18
103 -2.21e-17 -2.36e-17 -1.53e-17 -1.37e-17  1.95e-17 -2.94e-02  1.09e-17
104 -3.62e-18 -5.95e-18 -9.16e-18 -2.93e-18  1.61e-17 -2.94e-02  1.02e-17
105  1.27e-17  5.05e-18  1.43e-18 -4.96e-19 -1.01e-17 -6.10e-18  9.03e-19
106 -2.01e-18 -2.44e-18  1.18e-18  2.34e-18 -1.25e-18  7.27e-18 -1.00e-18
107 -2.78e-18 -4.54e-18 -3.40e-18 -4.13e-18  3.56e-18  7.05e-18  3.11e-18
108 -1.12e-18  2.02e-18  7.04e-18  1.03e-18 -8.67e-18 -9.31e-18 -4.20e-18
     dfb.vT.4 dfb.vYP.4 dfb.vD.10 dfb.vN.10 dfb.vPÑ.10 dfb.vT.10 dfb.vYP.10
1    3.96e-01  3.96e-01  3.96e-01  3.96e-01   3.96e-01  3.96e-01   3.96e-01
2   -5.03e-01 -5.03e-01  1.39e-14  7.99e-15   8.70e-15  7.86e-15   8.79e-15
3   -1.54e-15 -2.92e-16  1.07e+00  1.07e+00   1.07e+00  1.07e+00   1.07e+00
4    2.76e-15  2.99e-15  4.88e-15  3.86e-15   6.53e-15  4.36e-15   4.88e-15
5    4.65e-16  2.35e-16 -9.36e-16 -4.42e-16  -4.67e-16 -2.83e-16  -3.48e-16
6   -6.01e-16 -4.86e-16 -1.90e-15 -9.32e-16  -5.33e-16 -1.17e-15  -9.72e-16
7    5.03e-02  5.03e-02  5.03e-02  5.03e-02   5.03e-02  5.03e-02   5.03e-02
8   -6.50e-02 -6.50e-02 -9.81e-16 -5.23e-16  -6.23e-16 -5.93e-16  -6.62e-16
9   -2.02e-16 -1.92e-16  2.67e-01  2.67e-01   2.67e-01  2.67e-01   2.67e-01
10  -4.13e-17 -6.08e-17 -1.02e-16 -6.95e-17  -1.40e-16 -8.07e-17  -9.63e-17
11   4.22e-17  1.15e-16  1.51e-16  1.28e-16   9.03e-17  9.20e-17   1.70e-16
12   4.53e-16  5.19e-16  5.03e-16  3.25e-16   3.09e-16  3.23e-16   4.27e-16
13  -4.48e-01 -4.48e-01 -4.48e-01 -4.48e-01  -4.48e-01 -4.48e-01  -4.48e-01
14   5.71e-01  5.71e-01  5.36e-15  2.44e-15   2.70e-15  1.97e-15   1.97e-15
15  -1.79e-15 -7.16e-16 -1.41e+00 -1.41e+00  -1.41e+00 -1.41e+00  -1.41e+00
16   4.01e-15  4.80e-15  4.30e-15  3.60e-15   4.90e-15  3.64e-15   4.33e-15
17   7.04e-16  5.09e-16  8.58e-17  6.26e-16   9.83e-16  8.83e-16   6.09e-16
18   3.06e-16  2.77e-16  3.84e-16  1.13e-15   8.42e-16  9.98e-16   9.89e-16
19   1.37e-16 -1.18e-01 -1.04e-17 -3.87e-17   2.14e-18 -1.55e-17  -1.18e-01
20   1.72e-16  8.10e-02  1.09e-16  8.22e-17   1.07e-16  1.51e-16   8.99e-17
21   2.10e-19  6.03e-18 -1.90e-18 -6.80e-19  -3.52e-18 -9.69e-19  -7.36e-03
22   6.41e-16  9.08e-16  7.47e-16  4.55e-16   2.48e-16  5.05e-16   6.56e-16
23   3.70e-18 -5.92e-18  2.27e-17  1.21e-17   3.86e-17 -1.15e-18  -6.33e-18
24  -4.60e-17 -4.82e-17  7.41e-18 -1.15e-17  -6.89e-18 -2.67e-17  -1.84e-17
25   2.87e-17  4.05e-02  3.83e-17  3.19e-17   6.71e-17  5.06e-17   4.05e-02
26  -7.12e-19  1.10e-02 -3.87e-18 -5.28e-19  -4.96e-18 -4.10e-18   1.62e-19
27   5.82e-18  1.03e-17  4.94e-18  2.43e-18   3.67e-18  7.27e-19  -1.10e-02
28  -7.00e-17 -6.24e-17 -1.36e-16 -1.10e-16  -1.10e-16 -1.26e-16  -1.38e-16
29  -2.26e-18 -1.30e-17  7.33e-18  1.03e-17   2.62e-17  1.20e-17  -3.68e-18
30   7.24e-18  1.76e-17 -1.13e-18  2.58e-17   5.87e-18  4.37e-17   5.62e-17
31  -8.97e-17  7.73e-02 -9.72e-18 -5.17e-18   2.00e-17 -4.07e-17   7.73e-02
32  -5.94e-18 -9.20e-02  3.75e-17  2.20e-17   5.98e-18  2.32e-17   3.59e-17
33  -3.42e-18 -9.59e-18  8.26e-19 -1.39e-18   3.09e-18  2.42e-18   1.84e-02
34   5.47e-17  1.55e-16  5.08e-16  2.92e-16   3.67e-16  2.92e-16   4.70e-16
35   1.20e-16  1.34e-16  8.57e-17  9.42e-17   8.88e-17  1.09e-16   1.36e-16
36   1.50e-17 -2.30e-17  6.82e-18 -1.62e-17   8.81e-18 -4.37e-17  -8.09e-17
37   1.66e-16  1.16e-16  2.22e-17 -2.84e-17  -4.73e-01 -3.48e-17  -5.07e-17
38  -7.24e-17 -1.37e-16  6.48e-18  2.56e-17   5.91e-18  4.44e-17  -1.48e-17
39   1.43e-16  3.52e-16  1.42e-16  2.06e-16  -1.71e+00 -2.04e-16  -2.19e-16
40   4.96e-17  9.95e-17 -1.90e-16 -9.44e-17  -1.19e-16 -4.85e-17   2.87e-17
41  -2.19e-16 -1.97e-16  1.18e-16  1.94e-16   3.31e-16  8.74e-17   1.54e-16
42  -2.08e-16 -2.83e-16 -4.64e-17  1.71e-17  -6.65e-17  3.32e-17   1.13e-17
43  -1.62e-16 -1.38e-16  4.97e-17  9.43e-17   5.23e-01  1.03e-16   9.40e-17
44   8.83e-17  1.26e-16  4.92e-17  3.68e-17   3.97e-17  1.22e-17   4.68e-17
45  -7.03e-17 -1.07e-16 -9.10e-17 -1.20e-16   5.69e-01 -2.81e-18   3.14e-17
46  -2.41e-16 -3.10e-16  3.58e-16 -2.55e-18  -3.90e-17 -5.51e-17  -2.28e-16
47   2.44e-16  1.88e-16 -3.97e-17 -8.16e-17  -2.36e-16 -1.43e-17  -1.12e-16
48   2.55e-16  3.06e-16  1.24e-16  5.06e-17   1.22e-16  3.28e-17   2.81e-17
49   1.55e-17  1.30e-17 -5.09e-18 -4.31e-18  -4.78e-02 -8.83e-18  -8.16e-18
50   2.03e-18  3.03e-18  1.12e-18  6.99e-19   9.22e-19  1.55e-19   1.05e-18
51  -1.06e-16 -1.75e-16 -1.96e-16 -2.63e-16   9.72e-01  8.07e-18   6.26e-17
52   1.31e-16  1.80e-16 -2.32e-16 -3.24e-17   1.56e-17  1.91e-17   1.29e-16
53  -1.46e-18 -1.14e-18  1.99e-19  5.89e-19   1.32e-18  1.38e-19   7.30e-19
54  -2.42e-17 -2.96e-17 -1.19e-17 -1.92e-18  -9.41e-18 -2.49e-18  -2.25e-18
55  -9.68e-16 -9.43e-16 -1.14e-01 -9.01e-17  -8.95e-17 -1.05e-16  -1.21e-16
56  -3.74e-16 -3.48e-16 -5.95e-18  8.48e-18   6.49e-18  3.39e-17   2.78e-17
57  -9.41e-17 -7.72e-17  4.78e-02 -1.04e-17  -1.41e-17 -6.33e-18  -6.57e-18
58   1.18e-15  9.03e-16  1.27e-16  7.16e-17   4.11e-17  8.04e-17  -2.53e-17
59  -1.73e-16 -1.34e-16 -2.23e-17 -1.81e-17  -2.15e-17 -2.68e-17  -1.72e-17
60  -2.26e-16 -1.87e-16  1.71e-17 -3.57e-17  -1.49e-17 -2.42e-17  -2.15e-17
61  -3.28e-16 -3.12e-16 -6.99e-02 -3.01e-17  -2.97e-17 -3.95e-17  -4.98e-17
62  -9.25e-17 -9.65e-17 -1.26e-17 -1.59e-17  -1.56e-17 -1.98e-17  -1.85e-17
63   1.28e-16  1.52e-16  6.99e-02  9.90e-18   4.46e-18  1.53e-17   1.45e-17
64  -3.52e-16 -4.28e-16 -2.02e-17 -4.43e-17  -5.32e-17 -4.06e-17  -6.94e-17
65   4.93e-17  6.01e-17  5.27e-18  4.16e-18   3.22e-18  1.55e-18   4.06e-18
66   1.07e-16  1.25e-16  2.73e-17  3.54e-18   1.30e-17  8.42e-18   9.27e-18
67   8.55e-16  8.14e-16  1.84e-01  8.09e-17   7.97e-17  1.06e-16   1.33e-16
68  -4.82e-16 -5.03e-16 -6.04e-17 -7.94e-17  -7.80e-17 -9.90e-17  -9.23e-17
69  -2.21e-16 -2.63e-16 -1.18e-01 -1.57e-17  -6.64e-18 -2.48e-17  -2.32e-17
70   1.66e-15  2.02e-15  8.76e-17  1.98e-16   2.39e-16  1.80e-16   3.12e-16
71  -2.31e-16 -2.81e-16 -1.80e-17 -1.81e-17  -1.39e-17 -6.03e-18  -1.74e-17
72  -3.51e-16 -4.09e-16 -9.02e-17 -9.95e-18  -4.05e-17 -2.54e-17  -2.79e-17
73  -4.17e-02  1.01e-17 -3.79e-17 -3.61e-17  -4.92e-17 -4.17e-02  -4.60e-17
74   2.70e-02  1.60e-18 -1.44e-18 -2.08e-18  -3.77e-18  3.92e-18  -3.46e-18
75   1.81e-17  1.33e-17  2.36e-17  2.67e-17   2.19e-17 -3.93e-02   8.00e-18
76   1.07e-17  2.31e-17  1.45e-17  2.44e-17   1.21e-17 -1.28e-17   2.19e-17
77   5.56e-18 -1.02e-18 -1.16e-17 -4.31e-18  -3.83e-18  1.08e-17  -8.36e-18
78   1.31e-17 -1.17e-18  2.29e-18  5.06e-18   5.55e-18  1.28e-17  -3.33e-18
79  -1.59e-02  4.12e-18 -1.04e-17 -1.02e-17  -1.39e-17 -1.59e-02  -1.14e-17
80   4.54e-02  3.45e-18  1.52e-17  1.47e-17   1.31e-17  1.58e-17   1.19e-17
81   2.08e-17  1.38e-17  4.23e-18  5.83e-18   2.66e-18 -4.29e-02  -7.99e-18
82  -1.24e-18 -1.51e-18  2.54e-18  1.79e-18   3.08e-18  2.59e-18   1.78e-18
83  -1.39e-18  1.74e-20 -2.37e-18 -4.68e-18  -4.81e-18 -5.87e-18  -3.26e-18
84  -3.54e-18  2.34e-19 -5.64e-18 -6.73e-18  -7.72e-18 -6.62e-18  -3.95e-18
85   5.77e-02 -1.53e-17  3.15e-17  2.98e-17   4.29e-17  5.77e-02   4.09e-17
86  -7.24e-02 -5.99e-18 -2.39e-17 -2.48e-17  -2.18e-17 -2.42e-17  -1.92e-17
87  -4.21e-17 -2.60e-17 -6.82e-18 -9.88e-18   0.00e+00  8.22e-02   1.56e-17
88  -2.37e-17 -1.88e-17  3.12e-17  2.44e-17   4.08e-17  3.02e-17   2.36e-17
89  -1.52e-18 -2.38e-19 -7.49e-18 -1.50e-17  -1.73e-17 -1.74e-17  -1.05e-17
90  -3.86e-18  2.19e-19 -8.61e-18 -1.06e-17  -1.21e-17 -9.26e-18  -6.19e-18
91   0.00e+00  0.00e+00  0.00e+00  0.00e+00   0.00e+00  0.00e+00   0.00e+00
92  -2.63e-17 -2.90e-17  2.63e-18  5.49e-18   7.87e-19  2.16e-18  -6.03e-20
93   1.23e-17  7.52e-18  0.00e+00 -5.89e-02  -4.43e-18 -2.78e-18   4.27e-18
94  -5.50e-18  2.54e-18 -2.72e-17 -1.31e-17  -2.76e-17 -8.89e-18  -1.59e-17
95  -1.32e-17 -4.63e-18  7.92e-18  1.55e-17   1.65e-17  4.20e-18   1.63e-17
96   0.00e+00  0.00e+00  0.00e+00  0.00e+00   0.00e+00  0.00e+00   0.00e+00
97  -1.44e-17 -1.24e-17 -1.30e-17  2.94e-02  -1.03e-17 -8.29e-18  -1.64e-17
98   1.90e-17  2.08e-17  9.49e-18  9.13e-18   1.09e-17  9.53e-18   1.18e-17
99  -6.20e-18 -4.53e-18 -5.85e-18  2.21e-02  -4.01e-18 -4.37e-18  -7.48e-18
100 -4.13e-18 -1.61e-17 -8.24e-18 -4.24e-17  -3.70e-18 -2.75e-17  -2.13e-17
101  1.62e-17  9.93e-18  1.33e-17  1.07e-17   7.85e-18  1.66e-17   8.78e-18
102  3.95e-18  3.08e-18  3.22e-18  4.37e-18   2.11e-18  6.07e-19   9.57e-19
103  1.48e-17  1.30e-17  1.47e-17 -2.94e-02   1.32e-17  1.08e-17   1.95e-17
104  1.23e-17  1.33e-17  3.81e-18  3.65e-18   4.34e-18  3.86e-18   4.78e-18
105 -9.85e-18 -6.77e-18 -8.67e-18  3.68e-02  -3.05e-18 -4.16e-18  -8.62e-18
106  5.47e-19  3.44e-18 -2.52e-18  7.03e-18  -3.35e-18  3.75e-18   1.19e-18
107  4.14e-18  2.24e-18  2.07e-18  1.34e-18  -3.92e-20  2.64e-18   8.58e-20
108 -3.57e-18 -2.45e-18 -7.26e-19 -2.25e-18   7.97e-19  1.89e-18   2.12e-18
    dfb.vD.12 dfb.vN.12 dfb.vPÑ.12 dfb.vT.12 dfb.vYP.12 dfb.vD.15 dfb.vN.15
1    3.96e-01  3.96e-01   3.96e-01  3.96e-01   3.96e-01  3.96e-01  3.96e-01
2    1.39e-14  8.02e-15   8.86e-15  7.84e-15   8.97e-15  1.43e-14  8.27e-15
3    3.73e-15  1.41e-15   1.35e-15  6.78e-16   1.24e-15  3.61e-15  1.48e-15
4    5.90e-01  5.90e-01   5.90e-01  5.90e-01   5.90e-01  4.33e-15  3.32e-15
5   -5.62e-16 -2.27e-18   5.05e-18  2.45e-16   2.58e-16 -3.21e-01 -3.21e-01
6   -1.42e-15 -6.81e-16  -2.03e-16 -9.59e-16  -6.08e-16 -1.35e-15 -4.35e-16
7    5.03e-02  5.03e-02   5.03e-02  5.03e-02   5.03e-02  5.03e-02  5.03e-02
8   -9.54e-16 -5.17e-16  -6.15e-16 -5.20e-16  -6.51e-16 -9.05e-16 -4.76e-16
9   -1.17e-15 -5.41e-16  -8.88e-16 -9.45e-16  -1.08e-15 -1.21e-15 -8.29e-16
10   3.80e-02  3.80e-02   3.80e-02  3.80e-02   3.80e-02 -2.41e-17  2.11e-17
11   2.13e-16  2.26e-16   1.54e-16  1.54e-16   2.34e-16 -6.50e-02 -6.50e-02
12   8.12e-16  5.52e-16   5.05e-16  4.61e-16   6.17e-16  5.49e-16  3.45e-16
13  -4.48e-01 -4.48e-01  -4.48e-01 -4.48e-01  -4.48e-01 -4.48e-01 -4.48e-01
14   4.57e-15  1.46e-15   1.60e-15  1.25e-15   1.28e-15  5.36e-15  2.20e-15
15   7.56e-16 -4.18e-16  -8.56e-16 -1.65e-15  -1.39e-15 -8.64e-16 -1.65e-15
16  -6.31e-01 -6.31e-01  -6.31e-01 -6.31e-01  -6.31e-01  5.48e-15  5.16e-15
17  -5.60e-16 -2.97e-16   4.03e-16 -5.46e-17  -1.44e-16  3.87e-01  3.87e-01
18  -1.44e-15 -7.31e-16  -6.90e-16 -4.49e-16  -6.06e-16  3.47e-16  8.50e-16
19   4.14e-16  3.76e-16   3.50e-16  3.93e-16  -1.18e-01  6.07e-17  4.66e-17
20   1.52e-16  1.07e-16   1.24e-16  2.14e-16   1.11e-16  8.92e-17  5.74e-17
21  -8.39e-18 -7.15e-18  -7.97e-18 -7.03e-18  -7.90e-19 -3.14e-18 -2.89e-18
22   1.09e-15  8.55e-16   5.29e-16  7.09e-16  -3.26e-01  1.09e-15  5.88e-16
23   1.07e-16  7.90e-17   1.02e-16  8.50e-17   7.54e-17  4.88e-18 -8.29e-18
24  -1.38e-18 -2.46e-17  -3.31e-18 -2.25e-17  -4.65e-17 -3.92e-17 -5.57e-17
25  -2.50e-17 -3.95e-17   1.30e-17  0.00e+00   4.05e-02  5.19e-17  3.81e-17
26  -9.40e-18 -6.37e-18  -1.12e-17 -1.29e-17  -4.81e-18 -1.01e-17 -6.21e-18
27   1.03e-17  6.22e-18   8.21e-18  8.87e-18   8.71e-18  1.09e-17  1.07e-17
28  -1.34e-16 -1.12e-16  -1.46e-16 -1.44e-16  -8.47e-02 -1.21e-16 -7.23e-17
29  -6.16e-18 -6.42e-18   1.19e-17 -2.07e-17  -1.47e-17  8.95e-17  8.85e-17
30  -6.98e-17 -3.27e-17  -3.27e-17 -1.54e-17  -1.37e-17 -2.55e-17  3.48e-18
31  -1.53e-16 -1.59e-16  -1.22e-16 -1.58e-16   7.73e-02 -6.75e-19  2.02e-18
32   9.15e-17  8.13e-17   6.22e-17  1.05e-16   8.17e-17  4.14e-17  3.81e-17
33  -7.93e-18 -5.88e-18  -3.95e-18 -1.03e-17  -7.38e-18 -3.17e-18 -5.60e-18
34   4.92e-16  2.94e-16   5.80e-16  3.92e-16   4.12e-01  4.14e-16  3.12e-17
35   1.20e-16  1.37e-16   1.20e-16  1.83e-16   1.52e-16  1.21e-16  1.59e-16
36   1.54e-16  1.15e-16   8.89e-17  8.57e-17   5.44e-17  1.90e-17  1.36e-17
37   1.38e-15  1.42e-15  -4.73e-01  1.38e-15   1.28e-15  8.53e-17 -3.11e-17
38   1.63e-16  2.21e-16   1.62e-16  2.15e-16   9.72e-17  6.76e-17  9.28e-17
39  -6.56e-16 -9.45e-16  -8.82e-16 -8.08e-16  -8.03e-16 -4.32e-17 -2.17e-16
40  -2.50e-16 -1.45e-16  -5.19e-01 -2.90e-16  -4.35e-17 -8.75e-17 -4.07e-17
41   3.10e-16  3.32e-16   5.50e-16  2.16e-16   1.88e-16  2.21e-16  2.52e-16
42   1.36e-16  1.78e-16  -1.78e-17  2.72e-16   1.37e-16  3.82e-17  4.05e-17
43  -8.31e-16 -8.93e-16   5.23e-01 -8.12e-16  -7.36e-16 -2.75e-18  1.55e-16
44   4.53e-16  3.88e-16   4.56e-16  3.98e-16   4.84e-16  1.56e-17 -8.29e-18
45  -5.62e-16 -4.55e-16  -4.88e-16 -5.05e-16  -4.70e-16 -8.97e-17 -3.26e-17
46  -1.70e-15 -1.99e-15   1.79e+00 -1.43e-15  -2.16e-15 -2.53e-17 -1.89e-16
47   5.07e-16  4.96e-16   2.75e-16  5.89e-16   5.78e-16 -1.38e-16 -1.17e-16
48   6.16e-16  5.48e-16   7.69e-16  4.60e-16   5.75e-16  4.56e-17  2.85e-17
49   7.89e-17  8.91e-17  -4.78e-02  8.27e-17   7.46e-17  1.51e-18 -7.87e-18
50   9.32e-18  7.67e-18   9.25e-18  7.91e-18   1.03e-17 -2.65e-19 -8.97e-19
51  -7.93e-16 -6.07e-16  -6.57e-16 -6.93e-16  -6.54e-16 -9.57e-17  5.28e-18
52   9.01e-16  1.04e-15  -1.08e+00  6.80e-16   1.15e-15 -4.86e-17  4.67e-17
53  -2.51e-18 -2.35e-18  -1.07e-18 -3.01e-18  -3.03e-18  7.63e-19  8.48e-19
54  -5.12e-17 -4.28e-17  -6.48e-17 -3.56e-17  -4.81e-17 -2.24e-18  2.01e-18
55  -1.14e-01 -7.30e-17  -6.64e-17 -9.84e-17  -1.73e-16 -1.14e-01 -7.76e-17
56   1.73e-18  9.16e-18  -1.03e-18  2.20e-17   3.20e-17  1.86e-18 -1.38e-18
57  -1.11e-17 -8.54e-18  -2.00e-17 -1.49e-17  -6.76e-18 -5.40e-18 -1.02e-17
58  -6.36e-01  1.93e-16   1.35e-16  5.20e-17  -2.95e-16  2.64e-16  2.43e-16
59  -4.39e-17 -2.83e-17  -2.59e-17 -3.65e-17  -1.68e-17  9.20e-02 -2.89e-17
60  -5.43e-17 -3.50e-17  -2.41e-17 -2.16e-17  -1.92e-17 -2.94e-17 -5.56e-17
61  -6.99e-02 -1.78e-17  -1.30e-17 -3.29e-17  -8.11e-17 -6.99e-02 -1.67e-17
62  -1.47e-17 -1.71e-17  -1.58e-17 -1.94e-17  -1.97e-17 -1.67e-17 -1.76e-17
63   8.75e-18  1.44e-17  -1.61e-18  5.57e-18   1.51e-17  2.04e-17  1.60e-17
64  -1.81e-01 -1.47e-17  -3.31e-17 -5.59e-17  -1.48e-16  1.91e-18 -1.08e-17
65   3.42e-18  1.99e-18   2.93e-18 -1.38e-19   4.50e-18  2.58e-02  3.29e-18
66  -5.42e-18  5.33e-18   1.09e-17  1.18e-17   1.10e-17  1.32e-17 -8.88e-19
67   1.84e-01  4.18e-17   2.80e-17  8.23e-17   2.07e-16  1.84e-01  4.35e-17
68  -7.55e-17 -9.30e-17  -8.78e-17 -1.04e-16  -1.08e-16 -8.85e-17 -9.05e-17
69  -1.50e-17 -2.76e-17  -1.35e-18 -1.22e-17  -2.99e-17 -3.63e-17 -2.72e-17
70   8.33e-01  9.11e-17   1.81e-16  2.78e-16   7.16e-16  4.16e-18  5.16e-17
71  -1.14e-17 -1.24e-17  -1.75e-17 -2.20e-18  -2.50e-17 -1.18e-01 -1.53e-17
72   9.18e-18 -2.21e-17  -4.09e-17 -4.21e-17  -4.20e-17 -5.42e-17  2.41e-18
73   2.24e-17  2.79e-17   8.02e-18 -4.17e-02   3.93e-17 -5.43e-17 -5.06e-17
74   1.05e-18  1.98e-18  -9.18e-19  3.93e-18   2.92e-18 -7.14e-18 -5.89e-18
75   7.26e-18  7.28e-18   8.22e-18  1.06e-17   5.34e-18  1.95e-17  1.87e-17
76  -3.74e-18  1.56e-18  -3.86e-17 -1.20e-01  -8.44e-18  6.28e-17  6.18e-17
77   1.48e-18 -7.99e-18  -1.45e-18  1.52e-17  -3.33e-19 -1.65e-17 -1.78e-17
78   2.51e-18  2.08e-18   5.87e-18  1.58e-17  -6.06e-18 -9.97e-18 -7.90e-18
79   5.46e-18  7.92e-18   0.00e+00 -1.59e-02   1.37e-17 -1.20e-17 -1.11e-17
80  -1.16e-18  1.21e-18  -3.50e-18  2.18e-18   1.19e-18  1.64e-17  1.87e-17
81   1.07e-17  9.96e-18   1.08e-17  1.58e-17   9.36e-18 -5.58e-18 -6.60e-18
82   6.66e-19  2.62e-20   3.30e-18  8.59e-03  -1.02e-19  8.87e-19  9.91e-19
83   7.05e-19  2.24e-18   1.39e-18 -2.16e-18   1.19e-18 -5.60e-18 -6.03e-18
84   4.04e-19  3.78e-19  -1.35e-18 -3.87e-18   3.49e-18 -4.23e-18 -4.86e-18
85  -2.41e-17 -3.41e-17  -7.39e-18  5.77e-02  -4.86e-17  4.50e-17  3.83e-17
86   3.44e-18 -1.35e-18   5.67e-18 -2.15e-18  -6.16e-19 -2.13e-17 -2.65e-17
87  -2.23e-17 -1.97e-17  -2.09e-17 -3.17e-17  -1.94e-17  5.20e-18  8.91e-18
88   5.26e-18  3.41e-19   4.30e-17  1.12e-01  -3.30e-18  4.08e-18  7.82e-18
89   3.16e-18  8.59e-18   3.43e-18 -6.49e-18   4.53e-18 -1.42e-17 -1.50e-17
90   1.14e-18  1.27e-18  -1.74e-18 -4.80e-18   5.76e-18 -4.90e-18 -6.15e-18
91   0.00e+00  0.00e+00   0.00e+00  0.00e+00   0.00e+00  0.00e+00  0.00e+00
92  -6.82e-18  8.88e-19  -5.79e-18 -6.77e-18  -1.11e-17 -1.29e-17 -8.36e-18
93   1.38e-20 -7.52e-18  -3.50e-18  3.03e-18  -6.54e-19  8.45e-19 -1.53e-18
94  -3.22e-17 -1.18e-01  -3.27e-17 -1.13e-17   1.91e-18 -9.82e-18 -2.79e-17
95  -5.50e-18  3.76e-18  -1.52e-17 -1.70e-17  -3.94e-18  9.97e-18  1.03e-01
96   0.00e+00  0.00e+00   0.00e+00  0.00e+00   0.00e+00  0.00e+00  0.00e+00
97  -1.16e-17  2.94e-02  -8.22e-18 -8.83e-18  -1.68e-17 -6.65e-18  2.94e-02
98   7.27e-18  5.82e-18   6.60e-18  6.86e-18   9.55e-18  1.16e-17  1.13e-17
99  -1.59e-18 -3.54e-19  -2.53e-19 -2.54e-18  -1.19e-18 -2.25e-18 -2.55e-18
100  0.00e+00  1.62e-01   3.35e-17  5.24e-18  -1.31e-17 -7.09e-19  1.55e-17
101  8.16e-18  1.11e-17   1.77e-17  1.85e-17   8.34e-18 -5.22e-18 -8.10e-02
102  3.04e-18  5.82e-18   1.25e-18 -9.30e-19   1.48e-19  5.78e-18  1.48e-17
103  1.07e-17 -2.94e-02   8.31e-18  9.08e-18   1.71e-17  5.70e-18 -2.94e-02
104  4.64e-18  2.34e-18   4.30e-18  4.33e-18   6.04e-18  7.06e-18  6.03e-18
105 -2.40e-18  1.33e-18  -3.01e-19 -3.92e-18  -1.57e-18 -2.91e-18 -2.40e-18
106 -2.69e-18 -4.42e-02  -9.28e-18 -1.80e-18   3.09e-18 -8.16e-19 -6.42e-18
107  2.84e-18  2.91e-18   4.74e-18  4.86e-18   2.03e-18 -7.12e-19 -2.21e-02
108 -3.10e-18 -5.65e-18  -1.16e-18  1.18e-18   1.80e-19 -5.22e-18 -1.42e-17
    dfb.vPÑ.15 dfb.vT.15 dfb.vYP.15 dfb.vD.16 dfb.vN.16 dfb.vPÑ.16 dfb.vT.16
1     3.96e-01  3.96e-01   3.96e-01  3.96e-01  3.96e-01   3.96e-01  3.96e-01
2     9.23e-15  8.13e-15   9.24e-15  1.43e-14  8.28e-15   9.21e-15  8.16e-15
3     1.15e-15  6.10e-16   1.32e-15  3.71e-15  1.68e-15   1.52e-15  1.05e-15
4     5.52e-15  3.68e-15   3.98e-15  4.93e-15  4.02e-15   6.34e-15  4.41e-15
5    -3.21e-01 -3.21e-01  -3.21e-01 -7.40e-16 -4.70e-16  -2.92e-16 -1.38e-16
6     2.36e-16 -7.23e-16  -2.01e-16 -3.81e-01 -3.81e-01  -3.81e-01 -3.81e-01
7     5.03e-02  5.03e-02   5.03e-02  5.03e-02  5.03e-02   5.03e-02  5.03e-02
8    -5.65e-16 -4.87e-16  -5.90e-16 -1.05e-15 -6.15e-16  -7.31e-16 -6.16e-16
9    -8.63e-16 -8.75e-16  -1.08e-15 -9.75e-16 -5.72e-16  -5.81e-16 -6.01e-16
10   -5.87e-17  1.70e-17   4.87e-18 -1.01e-16 -7.02e-17  -1.49e-16 -7.55e-17
11   -6.50e-02 -6.50e-02  -6.50e-02  2.10e-16  1.74e-16   1.55e-16  1.40e-16
12    3.61e-16  3.00e-16   3.79e-16 -1.24e-01 -1.24e-01  -1.24e-01 -1.24e-01
13   -4.48e-01 -4.48e-01  -4.48e-01 -4.48e-01 -4.48e-01  -4.48e-01 -4.48e-01
14    2.53e-15  1.85e-15   1.82e-15  4.78e-15  1.61e-15   2.06e-15  1.33e-15
15   -1.70e-15 -2.87e-15  -2.15e-15 -3.06e-16 -1.08e-15  -1.50e-15 -2.42e-15
16    6.55e-15  5.26e-15   6.27e-15  4.68e-15  4.47e-15   5.66e-15  4.32e-15
17    3.87e-01  3.87e-01   3.87e-01  4.74e-16  7.34e-16   9.81e-16  9.86e-16
18    5.80e-16  9.59e-16   9.89e-16  5.09e-01  5.09e-01   5.09e-01  5.09e-01
19    1.76e-16  1.19e-16  -1.18e-01  2.19e-16  1.86e-16   2.75e-16  2.16e-16
20    9.06e-17  1.56e-16   5.14e-17  1.11e-16  6.05e-17   7.50e-17  1.47e-16
21   -5.72e-18 -3.12e-18  -1.18e-18 -2.96e-18  1.04e-18  -4.37e-19  1.32e-18
22    4.03e-16  5.64e-16   7.21e-16  9.39e-16  5.38e-16   3.41e-16  5.40e-16
23    5.40e-17  0.00e+00   6.63e-02  8.03e-17  7.13e-17   5.98e-17  5.46e-17
24   -7.12e-17 -5.04e-17  -7.72e-17  3.24e-17 -2.05e-17  -1.88e-17 -3.31e-17
25    8.41e-17  7.88e-17   4.05e-02  4.59e-17  2.36e-17   4.66e-17  5.39e-17
26   -1.24e-17 -1.45e-17  -9.22e-18 -7.08e-18 -3.08e-18  -6.64e-18 -6.46e-18
27    1.39e-17  1.13e-17   1.72e-17  1.40e-17  8.88e-18   7.50e-18  6.64e-18
28   -5.43e-17 -9.42e-17  -5.69e-17 -1.20e-16 -8.48e-17  -9.90e-17 -1.06e-16
29    1.16e-16  8.12e-17   6.26e-02 -5.88e-17 -5.13e-17  -1.20e-17 -3.49e-17
30   -4.55e-17  4.70e-18   1.04e-17 -4.55e-17 -1.65e-17  -1.59e-17  2.60e-17
31    1.30e-17 -5.57e-17   7.73e-02 -6.63e-17 -7.70e-17  -9.06e-17 -1.35e-16
32    5.53e-18  4.02e-17   3.70e-17  5.50e-17  2.59e-17  -9.73e-18  1.91e-17
33   -2.40e-18 -2.72e-18  -8.66e-18  2.16e-18  1.65e-18   5.41e-18  3.34e-18
34    9.85e-17  9.55e-17   1.04e-16  5.40e-16  2.21e-16   2.88e-16  1.93e-16
35    1.03e-16  1.77e-16  -1.29e-01  4.34e-17  2.94e-17   4.31e-17  2.34e-17
36    5.48e-17 -2.76e-17  -6.44e-17  6.45e-17  4.09e-17   6.58e-17  0.00e+00
37   -4.73e-01  7.35e-17   1.19e-16  6.33e-17 -3.60e-17  -4.73e-01 -7.32e-17
38    6.57e-17  7.33e-17   4.25e-17  5.45e-17  1.00e-16   5.95e-17  1.09e-16
39   -2.79e-16 -3.41e-16  -4.16e-16 -4.37e-16 -5.38e-16  -6.08e-16 -5.06e-16
40    9.55e-17 -6.03e-17  -9.05e-18 -6.32e-17 -2.72e-17   7.00e-17 -2.53e-17
41    5.89e-01  8.78e-17  -3.10e-17  2.96e-16  2.96e-16   4.21e-16  2.33e-16
42   -9.94e-17  1.47e-16   6.85e-17 -3.41e-17 -7.66e-17   5.04e-01  6.33e-17
43    5.23e-01  1.55e-17  -8.60e-17  4.33e-17  1.19e-16   5.23e-01  1.66e-16
44    2.30e-17  1.11e-17  -2.73e-18  3.58e-17 -1.52e-17   4.80e-17 -3.43e-17
45   -1.82e-17  8.21e-18   8.93e-17  3.20e-17  7.38e-17   6.73e-17  7.61e-17
46   -6.76e-16 -1.23e-16  -1.24e-16 -1.38e-16 -2.36e-16  -6.65e-16 -2.02e-16
47   -5.93e-01  2.13e-17   8.26e-17 -1.80e-16 -1.89e-16  -2.83e-16 -1.38e-16
48    1.62e-16 -6.01e-17  -2.77e-17  1.34e-16  1.49e-16  -5.62e-01  2.04e-17
49   -4.78e-02  1.21e-18   9.86e-18 -5.38e-18 -9.09e-18  -4.78e-02 -1.34e-17
50   -5.72e-19 -3.33e-19  -5.27e-19  5.46e-19 -8.17e-19   4.05e-19 -1.24e-18
51    6.95e-17  6.74e-17   1.93e-16  8.43e-17  1.65e-16   1.84e-16  1.65e-16
52    2.99e-16  1.50e-17   2.99e-17  5.09e-17  1.00e-16   3.27e-16  8.40e-17
53    3.68e-03  7.00e-20  -3.60e-19  1.23e-18  1.32e-18   2.01e-18  9.89e-19
54   -1.04e-17  8.94e-18   5.02e-18 -1.24e-17 -1.05e-17   5.52e-02 -3.55e-20
55   -8.56e-17 -8.14e-17  -7.06e-17 -1.14e-01 -1.03e-16  -1.25e-16 -1.24e-16
56   -2.12e-18  1.21e-17   1.54e-18  1.68e-16  1.79e-16   1.64e-16  2.10e-16
57   -1.59e-17 -1.12e-17  -6.00e-18 -1.17e-17 -1.49e-17  -1.15e-17 -1.70e-17
58    2.11e-16  2.17e-16   2.31e-16  1.96e-16  2.33e-16   2.15e-16  2.32e-16
59   -2.61e-17 -3.17e-17  -3.35e-17 -1.71e-17 -1.97e-17  -2.06e-17 -2.68e-17
60   -2.95e-17 -3.50e-17  -6.63e-17  1.22e-01 -5.69e-17  -2.13e-17 -3.48e-17
61   -2.12e-17 -2.00e-17  -1.18e-17 -6.99e-02 -3.50e-17  -4.88e-17 -4.91e-17
62   -1.77e-17 -1.93e-17  -1.84e-17 -4.06e-17 -4.54e-17  -4.29e-17 -5.00e-17
63    8.01e-18  1.35e-17   2.27e-17  5.59e-18  5.97e-18   1.10e-17  2.12e-18
64   -2.06e-17 -1.55e-17  -1.56e-17 -2.78e-18 -5.69e-18  -1.07e-17 -3.88e-18
65    4.19e-18  2.13e-18   2.21e-18  3.56e-18  4.71e-18   4.49e-18  2.42e-18
66    1.12e-17  7.65e-18  -5.32e-18  5.52e-02 -3.91e-18   1.23e-17  5.47e-18
67    5.52e-17  5.27e-17   3.05e-17  1.84e-01  8.93e-17   1.26e-16  1.28e-16
68   -9.13e-17 -9.84e-17  -9.48e-17 -2.04e-16 -2.35e-16  -2.22e-16 -2.57e-16
69   -1.40e-17 -2.28e-17  -3.86e-17 -7.51e-18 -1.20e-17  -2.00e-17 -4.63e-18
70    9.84e-17  7.20e-17   7.47e-17 -6.72e-19  3.99e-17   5.99e-17  2.54e-17
71   -1.97e-17 -9.84e-18  -1.05e-17 -1.44e-17 -2.35e-17  -2.20e-17 -1.21e-17
72   -3.68e-17 -2.46e-17   1.64e-17 -1.77e-01  9.65e-18  -4.15e-17 -1.91e-17
73   -5.95e-17 -4.17e-02  -3.83e-17 -1.30e-17 -1.16e-17  -1.47e-17 -4.17e-02
74   -8.77e-18 -4.01e-18  -2.77e-18 -2.10e-18 -4.16e-19  -2.13e-18  2.74e-18
75    2.31e-17  1.76e-17   2.50e-17 -4.25e-18 -3.76e-18  -3.57e-18 -5.62e-19
76    7.09e-17  4.87e-17   6.31e-17  6.77e-18  8.25e-18   6.00e-18  7.24e-18
77   -1.92e-17  5.64e-02  -1.82e-17  2.93e-18  9.60e-19   9.93e-19  6.81e-18
78   -6.34e-18 -4.51e-19  -1.58e-17  3.03e-18  3.03e-18   1.21e-17  3.43e-02
79   -1.30e-17 -1.59e-02  -5.69e-18 -4.83e-18 -4.28e-18  -5.01e-18 -1.59e-02
80    1.48e-17  1.72e-17   2.08e-17 -6.32e-19  3.50e-18  -8.34e-19  1.09e-17
81   -2.75e-18 -3.41e-18   3.29e-18 -7.39e-18 -8.08e-18  -6.50e-18 -6.55e-18
82    5.33e-19  1.05e-18   3.11e-19  6.47e-20  2.05e-19   9.13e-20  6.71e-19
83   -4.59e-18 -1.35e-02  -3.21e-18 -1.56e-18 -1.48e-18  -1.05e-18 -3.50e-18
84   -6.20e-18 -6.53e-18  -1.37e-18 -1.32e-18 -1.32e-18  -5.30e-18 -1.35e-02
85    4.70e-17  5.77e-02   2.40e-17  1.69e-17  1.49e-17   1.58e-17  5.77e-02
86   -1.94e-17 -2.07e-17  -2.89e-17  8.87e-19 -7.04e-18  -1.53e-18 -1.74e-17
87    4.37e-19 -1.11e-18  -1.12e-17  1.43e-17  1.71e-17   1.57e-17  1.26e-17
88    3.78e-19  3.32e-18  -2.59e-18  1.03e-18  4.92e-18   5.60e-18  8.86e-18
89   -1.46e-17 -4.29e-02  -7.67e-18 -5.04e-18 -5.57e-18  -5.05e-18 -1.12e-17
90   -7.66e-18 -6.46e-18  -8.86e-19 -2.25e-18 -2.25e-18  -9.00e-18 -2.09e-02
91    0.00e+00  0.00e+00   0.00e+00  0.00e+00  0.00e+00   0.00e+00  0.00e+00
92   -1.27e-17 -1.37e-17  -1.86e-17  9.15e-19  8.46e-18   8.08e-19  4.95e-18
93   -5.26e-18 -1.08e-18   2.21e-18 -3.81e-18 -8.18e-18  -9.52e-18 -6.64e-19
94   -1.27e-17 -9.99e-18  -4.26e-18 -1.63e-17 -2.27e-17  -1.62e-17 -7.56e-18
95   -7.40e-18  4.19e-18   1.66e-18 -4.03e-18 -1.43e-18   1.12e-18 -1.15e-17
96    0.00e+00  0.00e+00   0.00e+00  0.00e+00  0.00e+00   0.00e+00  0.00e+00
97   -8.48e-18 -3.23e-18  -1.25e-17 -9.87e-18  2.94e-02  -6.96e-18 -4.88e-18
98    1.14e-17  1.16e-17   1.48e-17  4.64e-18  2.14e-18   4.00e-18  1.21e-18
99    7.71e-20 -1.29e-18  -2.66e-18 -1.17e-18 -5.41e-19   1.33e-18 -1.84e-18
100   3.62e-18  1.29e-18  -7.57e-18  3.34e-18  4.77e-18   5.79e-18 -4.95e-18
101   1.28e-17  2.92e-18   5.41e-18  1.27e-17  1.44e-17   7.35e-18  1.67e-17
102   4.80e-18  1.20e-18   6.64e-18  4.38e-18 -2.94e-02   2.43e-19  1.16e-18
103   9.09e-18  3.84e-18   1.35e-17  9.87e-18 -2.94e-02   7.78e-18  5.96e-18
104   6.98e-18  7.12e-18   8.84e-18  2.11e-18  3.74e-19   1.85e-18 -2.71e-19
105   8.93e-19 -1.39e-18  -3.16e-18 -7.12e-19  4.15e-19   3.23e-18 -1.72e-18
106  -1.90e-18 -1.26e-18   5.35e-19 -2.39e-18 -2.88e-18  -2.80e-18 -2.70e-19
107   3.02e-18  3.42e-19   7.11e-19  2.72e-18  3.12e-18   1.39e-18  3.76e-18
108  -4.19e-18 -5.94e-19  -5.62e-18 -4.38e-18  2.94e-02   5.72e-19 -7.91e-20
    dfb.vYP.16  dfb.vC.2  dfb.vD.2  dfb.vN.2 dfb.vPÑ.2  dfb.vT.2 dfb.vYP.2
1     3.96e-01 -3.96e-01 -1.34e-15  1.49e-16  5.06e-16 -2.30e-16 -1.48e-17
2     9.24e-15 -5.03e-01  5.95e-15  6.62e-17  4.65e-16 -2.87e-16  3.43e-16
3     1.31e-15  1.07e+00  2.00e-15  6.23e-16 -4.43e-16 -1.01e-15  2.15e-16
4     4.52e-15  5.90e-01  1.16e-15 -6.30e-17  2.80e-15  3.48e-16  5.63e-16
5    -4.07e-16 -3.21e-01 -6.61e-16  4.06e-17  1.01e-16  6.87e-16  1.21e-16
6    -3.81e-01 -3.81e-01 -7.49e-16  4.09e-17  1.12e-16 -2.83e-16  2.09e-16
7     5.03e-02  5.03e-02  8.81e-17 -1.12e-17 -3.13e-17  2.98e-17 -6.85e-17
8    -7.26e-16  6.50e-02 -3.91e-16 -4.34e-18 -2.67e-17  3.52e-17 -3.11e-17
9    -8.46e-16 -2.67e-01 -2.81e-16 -9.05e-17 -4.21e-17  1.25e-16  3.76e-17
10   -1.08e-16 -3.80e-02 -3.94e-17  1.83e-18 -9.74e-17  3.78e-20 -8.17e-17
11    1.57e-16  6.50e-02  7.30e-17 -8.72e-18 -1.02e-17 -5.51e-17 -1.22e-17
12   -1.24e-01  1.24e-01  1.63e-16  1.30e-17 -1.78e-17  3.32e-17 -3.20e-17
13   -4.48e-01 -5.97e-16 -6.87e-16  7.11e-17  2.21e-16 -1.80e-16  4.61e-16
14    1.40e-15 -2.09e-15  3.58e-15  4.55e-17  2.54e-16 -1.66e-16  1.51e-16
15   -1.26e-15 -5.15e-15  1.16e-15  5.40e-16 -4.96e-16 -5.33e-16 -1.31e-15
16    5.03e-15 -2.47e-15  5.11e-16 -3.01e-18  1.23e-15  3.90e-16  1.15e-15
17    1.04e-15  6.12e-16 -3.48e-16 -6.38e-21  2.85e-17  4.51e-16 -6.37e-17
18    5.09e-01 -2.30e-31 -3.37e-16  6.48e-17  5.93e-17 -1.28e-16  1.26e-16
19   -1.18e-01  1.25e-16  7.30e-18 -8.42e-18  3.06e-17  2.53e-17 -1.18e-01
20    3.76e-17  2.52e-17 -5.97e-18  5.14e-19 -7.15e-18  3.10e-18 -8.10e-02
21    7.55e-18 -2.95e-18 -1.26e-18 -3.75e-19 -1.30e-19  1.27e-18  7.36e-03
22    7.41e-16 -3.05e-16 -7.86e-17 -2.37e-17 -8.83e-17  3.39e-17  3.26e-01
23    1.42e-16  4.16e-17  4.77e-18  2.91e-19 -1.22e-17  2.75e-18 -6.63e-02
24    6.63e-02  4.43e-17  5.33e-18  4.96e-18  9.40e-18  5.45e-18 -6.63e-02
25    4.05e-02 -1.38e-17 -2.18e-18  8.48e-20  1.37e-18  2.48e-18 -4.05e-02
26   -3.54e-19  4.64e-19 -1.20e-18  2.51e-19  3.04e-18 -1.00e-20  1.10e-02
27    9.91e-18 -1.08e-17  1.16e-18 -4.47e-19 -7.09e-19 -4.65e-18 -1.10e-02
28   -8.68e-17  1.97e-17  7.59e-18  4.57e-18 -2.36e-17 -4.19e-17 -8.47e-02
29   -7.42e-17  2.11e-17  3.10e-19 -1.09e-18 -1.54e-18  6.06e-18  6.26e-02
30    6.26e-02 -2.01e-17  1.82e-18  3.82e-18 -1.30e-18  3.79e-18  6.26e-02
31    7.73e-02 -1.21e-17  2.51e-19  2.88e-18  1.60e-17  1.89e-17  3.22e-17
32    6.64e-17 -6.43e-17 -7.10e-18  1.12e-18  1.53e-17 -8.89e-18 -8.43e-17
33   -3.54e-18  9.79e-18 -1.77e-18 -8.65e-19  6.90e-19 -1.79e-18  1.53e-18
34    2.78e-16 -5.65e-16 -8.56e-17  7.42e-18 -1.06e-16 -1.01e-16 -5.49e-16
35   -3.72e-17 -5.70e-17  1.50e-17 -2.25e-18 -7.27e-18  5.20e-18 -1.07e-17
36   -1.29e-01 -7.13e-17  2.08e-17  4.71e-18  2.76e-17  1.55e-17  7.51e-17
37   -1.08e-16  8.64e-16  1.01e-16 -2.63e-18 -4.73e-01  1.24e-17  2.84e-16
38    9.34e-17  3.71e-16 -5.19e-17  1.66e-17 -4.58e-01 -2.31e-17 -5.66e-17
39   -1.01e-15 -8.33e-16 -2.72e-16 -2.27e-16  1.71e+00  5.99e-17 -2.05e-17
40   -6.08e-18 -6.37e-17 -8.40e-17 -1.71e-17  5.19e-01  3.99e-17  1.04e-17
41    4.88e-16  6.19e-16  9.76e-17  3.63e-17 -5.89e-01  7.23e-17 -3.38e-16
42   -4.25e-17  2.30e-16  8.44e-17  2.39e-17 -5.04e-01 -3.89e-17  1.45e-16
43    2.07e-16  8.00e-17  6.12e-17  2.83e-17 -5.23e-01 -6.18e-17 -3.53e-16
44   -1.66e-17 -2.58e-16 -1.19e-17  2.13e-17 -4.47e-01 -1.81e-17 -1.87e-17
45    2.40e-16 -4.65e-17 -4.25e-17 -4.47e-17  5.69e-01  3.19e-17  1.37e-16
46   -2.77e-16 -8.82e-16 -1.13e-16 -1.07e-16  1.79e+00  1.46e-16 -1.31e-15
47   -3.93e-16 -2.00e-16  4.02e-17  1.32e-17 -5.93e-01  8.65e-17  5.21e-16
48    1.41e-16  3.55e-17  6.43e-17  2.47e-17 -5.62e-01 -1.77e-17 -2.24e-16
49   -1.67e-17 -7.98e-19 -5.70e-18  4.73e-19 -3.98e-18  4.97e-18  2.74e-17
50   -9.20e-19 -6.30e-18  8.10e-19 -3.19e-19 -4.53e-35 -9.48e-19 -1.97e-18
51    4.55e-16 -1.10e-16 -1.08e-16 -1.54e-17 -8.09e-17  9.84e-17  1.93e-16
52    1.18e-16  5.97e-16  1.08e-16 -1.82e-17 -9.03e-17 -1.16e-16  5.07e-16
53    2.61e-18  1.21e-18 -3.84e-19  1.99e-19 -6.13e-19 -2.28e-20 -3.74e-18
54   -1.13e-17 -3.93e-18 -8.33e-18  1.79e-18  4.60e-18  4.24e-18  2.95e-17
55   -1.20e-16 -6.43e-16 -1.14e-01 -2.95e-18  1.37e-17  1.62e-18 -2.54e-17
56    1.83e-16 -7.08e-16 -2.47e-01  7.68e-20  3.55e-17 -5.90e-20 -9.10e-18
57   -1.41e-17 -6.73e-17 -4.78e-02  4.32e-19  4.53e-18  9.06e-19 -1.36e-18
58    1.72e-16  1.56e-15  6.36e-01  1.53e-17 -8.78e-17  6.96e-18  3.43e-16
59   -3.81e-18 -2.08e-16 -9.20e-02 -1.08e-18  6.24e-18 -1.57e-18  6.04e-18
60   -2.40e-17 -2.62e-16 -1.22e-01 -1.33e-18  8.97e-18 -6.17e-19  4.90e-17
61   -4.58e-17 -1.75e-16  6.99e-02 -1.81e-18 -6.76e-18  9.92e-19 -6.01e-18
62   -4.60e-17 -1.34e-17 -4.05e-02 -1.26e-20  5.82e-18  9.65e-21 -2.92e-18
63    7.19e-18  1.25e-16  6.99e-02  6.31e-19 -3.94e-18  1.32e-18  3.66e-19
64   -2.29e-17 -1.25e-16 -1.81e-01  4.34e-18  1.80e-17  1.98e-18  9.02e-17
65    9.15e-18  2.28e-17  2.58e-02 -3.03e-19 -2.79e-18 -4.38e-19  3.96e-18
66    1.10e-17  5.48e-17  5.52e-02 -6.04e-19 -4.75e-18 -2.80e-19  4.04e-17
67    1.18e-16  4.34e-16 -1.53e-17  4.76e-18 -1.57e-18 -2.62e-18  2.62e-17
68   -2.38e-16 -8.59e-17  5.16e-17 -6.41e-20 -6.62e-18  4.92e-20 -3.99e-18
69   -1.40e-17 -2.20e-16 -1.03e-31 -1.06e-18 -8.55e-19 -2.23e-18 -4.33e-19
70    1.19e-16  6.85e-16  1.39e-16 -2.00e-17  4.22e-17 -9.12e-18 -4.63e-16
71   -4.37e-17 -1.20e-16 -9.81e-18  1.38e-18  5.15e-18  2.00e-18 -1.58e-17
72   -3.80e-17 -1.99e-16 -2.95e-17  1.94e-18  6.67e-18  8.98e-19 -1.02e-16
73   -1.00e-18 -9.20e-17  2.31e-19 -1.11e-18  1.94e-18 -4.17e-02 -2.91e-17
74    6.50e-19 -1.39e-17 -1.22e-18  2.15e-19  5.85e-19 -2.70e-02  3.12e-19
75   -4.72e-18  1.63e-17  8.82e-19 -1.20e-18 -1.11e-18  3.93e-02 -1.48e-17
76   -1.16e-17  1.00e-16 -2.39e-18  5.76e-19 -7.36e-18  1.20e-01 -5.02e-17
77    2.63e-21 -5.44e-17 -2.36e-19  1.10e-18 -1.39e-19 -5.64e-02  4.24e-18
78    4.96e-18 -3.04e-17 -1.50e-18  4.46e-19  7.17e-19 -3.43e-02 -1.11e-17
79   -5.18e-19 -2.22e-17  8.84e-20 -4.24e-19 -5.69e-19  1.59e-02 -1.15e-17
80    7.08e-19  1.37e-17 -2.05e-18  3.61e-19 -5.70e-19  4.54e-02 -8.03e-19
81   -4.80e-18 -1.72e-17  9.64e-19 -1.32e-18 -1.29e-18 -4.29e-02 -1.72e-17
82    7.53e-19 -1.38e-19  1.71e-19 -4.11e-20  2.48e-20  8.59e-03  3.39e-18
83    1.14e-19  2.65e-18  5.64e-20 -2.64e-19  6.57e-19 -1.35e-02 -1.52e-18
84   -1.83e-18  1.59e-18  5.89e-19 -1.75e-19 -3.06e-19 -1.35e-02  2.42e-18
85    9.02e-19  8.28e-17 -3.20e-19  1.53e-18 -1.66e-18  4.80e-18  3.46e-17
86   -2.35e-18 -1.86e-17  3.27e-18 -5.76e-19 -2.75e-19  1.81e-17 -4.49e-18
87    1.06e-17  2.93e-17 -1.85e-18  2.52e-18  8.46e-19 -6.85e-18  3.91e-17
88    1.17e-17 -6.84e-18  2.22e-18 -5.35e-19  4.83e-18 -2.79e-17  5.23e-17
89   -3.60e-19  8.31e-18  1.80e-19 -8.40e-19  8.73e-19  7.15e-18 -6.43e-18
90   -3.18e-18  2.40e-18  9.10e-19 -2.71e-19 -6.28e-20  1.74e-18  5.68e-18
91    0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
92   -6.96e-18  1.26e-17 -1.93e-18 -7.36e-02 -4.30e-18 -5.73e-20  3.98e-18
93   -9.64e-20 -1.44e-17  7.14e-19  5.89e-02  2.67e-18 -9.69e-19  5.17e-20
94   -2.00e-17  2.15e-17  5.71e-19  1.18e-01  1.59e-18 -2.69e-18 -1.15e-17
95    2.65e-18 -2.68e-17  7.85e-20 -1.03e-01 -1.11e-17  1.25e-19 -1.54e-17
96    0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
97   -1.06e-17  7.09e-18  4.90e-19 -2.94e-02 -3.04e-18 -1.42e-18 -2.91e-18
98    8.46e-18 -4.88e-18  1.16e-18 -4.42e-02 -3.54e-18  3.44e-20 -1.76e-18
99   -2.10e-18  5.15e-18 -2.68e-19  2.21e-02  1.34e-18  3.63e-19 -7.92e-19
100   1.18e-17 -3.15e-17 -7.85e-19  1.62e-01  6.93e-18  3.70e-18  2.24e-17
101   5.77e-18  2.59e-17 -6.17e-20 -8.10e-02  1.13e-19 -9.78e-20  2.33e-17
102  -2.85e-18 -9.62e-20  5.62e-19 -2.94e-02 -1.14e-18  3.63e-19  1.21e-18
103   1.20e-17 -4.60e-18 -4.90e-19  6.13e-35  8.36e-22  1.42e-18  1.45e-18
104   4.32e-18 -5.75e-18  7.72e-19 -2.60e-34 -1.29e-19  2.29e-20  2.77e-19
105  -1.86e-18  9.93e-18 -4.46e-19 -1.52e-34  6.45e-19  6.05e-19 -6.01e-19
106  -5.20e-18  6.97e-18  2.14e-19  7.35e-18 -2.18e-18 -1.01e-18 -3.63e-18
107   5.85e-19  5.20e-18 -1.68e-20 -1.84e-18  9.81e-19 -2.67e-20  4.69e-18
108   4.17e-18  2.59e-18 -5.62e-19 -5.11e-35  6.32e-19 -3.63e-19 -1.96e-20
     dfb.vC.3  dfb.vD.3  dfb.vN.3 dfb.vPÑ.3  dfb.vT.3 dfb.vYP.3     dffit
1   -3.96e-01 -1.39e-15  9.52e-17  5.89e-16 -2.61e-16  1.83e-16  9.14e-01
2   -5.03e-01  6.10e-15  5.29e-17  5.47e-16 -3.00e-16  3.68e-16  1.16e+00
3    1.07e+00  2.26e-15  7.68e-17 -4.49e-16 -1.02e-15  1.51e-16 -2.47e+00
4    5.90e-01  1.36e-15 -2.60e-17  2.40e-15  3.94e-16  7.58e-16 -1.36e+00
5   -3.21e-01 -7.39e-16 -4.24e-18  1.14e-16  5.01e-16 -1.32e-16  7.41e-01
6   -3.81e-01 -8.13e-16  1.52e-17  1.58e-16 -2.24e-16  5.58e-16  8.80e-01
7   -6.65e-17  9.13e-17 -8.61e-18 -3.45e-17  2.59e-17 -4.67e-17  1.16e-01
8    3.14e-16 -3.94e-16  2.94e-18 -1.48e-17  2.93e-17 -1.60e-17  1.50e-01
9   -3.40e-16 -2.58e-16 -4.99e-17 -1.68e-17  1.27e-16  1.21e-16 -6.17e-01
10   4.66e-17 -3.96e-17 -9.66e-19 -8.82e-17  3.04e-18 -7.61e-17 -8.78e-02
11   8.91e-17  8.00e-17 -4.74e-18 -1.91e-18 -6.29e-17 -5.21e-17  1.50e-01
12  -3.07e-16  1.38e-16  5.97e-18 -2.97e-17  3.71e-17 -1.01e-18  2.86e-01
13  -4.48e-01 -8.13e-16  4.55e-17  2.43e-16 -1.60e-16  3.91e-16 -1.03e+00
14  -5.71e-01  3.53e-15  2.72e-17  3.91e-16 -1.16e-16  3.34e-16 -1.32e+00
15   1.41e+00  1.58e-15  1.99e-16 -3.63e-16 -8.50e-16 -1.44e-15  3.25e+00
16   6.31e-01  7.26e-16  2.59e-18  1.05e-15  3.59e-16  1.16e-15  1.46e+00
17  -3.87e-01 -4.02e-16 -1.31e-17  4.22e-17  4.19e-16  2.24e-16 -8.94e-01
18  -5.09e-01 -4.86e-16 -3.05e-17  6.84e-17 -1.32e-16  5.71e-17 -1.18e+00
19   1.73e-16  2.60e-18 -1.57e-17  3.30e-17  1.52e-17 -1.18e-01  2.72e-01
20   6.42e-17 -5.66e-18  3.75e-18  6.37e-18  1.40e-17 -8.10e-02  1.87e-01
21   2.65e-18 -9.50e-19 -1.06e-18 -1.00e-18  1.42e-18  7.36e-03 -1.70e-02
22  -2.58e-16 -8.59e-17 -1.52e-17 -1.16e-16  3.57e-17  3.26e-01 -7.52e-01
23  -4.78e-18  3.29e-18  9.65e-18 -1.87e-18  2.32e-18 -6.63e-02  1.53e-01
24   5.57e-17  2.49e-18  3.45e-18  8.84e-18  3.38e-18 -6.63e-02  1.53e-01
25  -3.79e-17 -3.13e-18 -1.47e-18  4.53e-18  8.51e-19 -9.66e-18 -9.35e-02
26  -8.23e-18 -9.30e-19  1.42e-19  2.35e-18 -3.07e-18  1.94e-18  2.55e-02
27  -1.33e-18  9.62e-19 -9.76e-20 -3.17e-19 -2.83e-18  1.96e-17 -2.55e-02
28  -1.02e-17  9.94e-18 -3.17e-18 -2.38e-17 -3.01e-17  1.54e-17 -1.96e-01
29  -4.51e-18 -2.78e-19 -3.40e-18  4.34e-19 -1.32e-17 -2.64e-17  1.44e-01
30   2.26e-17  2.39e-18  3.42e-18  1.25e-18 -4.52e-18  5.05e-17  1.44e-01
31  -5.02e-17 -5.43e-18 -4.25e-18  1.54e-17  2.61e-17 -7.73e-02 -1.79e-01
32   2.43e-17 -1.57e-17  6.45e-19  1.40e-17 -2.68e-18 -9.20e-02 -2.13e-01
33  -4.86e-18  1.01e-19 -2.41e-18  6.75e-19 -1.80e-18  1.84e-02  4.25e-02
34  -5.45e-16 -6.61e-17  1.46e-18 -1.65e-16 -9.43e-17  4.12e-01  9.52e-01
35   4.65e-17  8.04e-18 -2.78e-18 -4.66e-18 -2.87e-17 -1.29e-01 -2.98e-01
36  -4.65e-17  1.00e-17  9.48e-18  2.67e-17  3.66e-18 -1.29e-01 -2.98e-01
37   1.14e-15  8.56e-17 -3.26e-17 -4.73e-01  4.16e-17 -1.21e-16  1.09e+00
38  -6.97e-17 -2.04e-16 -1.58e-17 -4.58e-01  1.51e-17 -1.21e-16  1.06e+00
39   1.37e-17 -1.13e-16 -1.67e-16  1.71e+00 -8.91e-17 -5.23e-16 -3.95e+00
40  -1.58e-16 -2.37e-17  5.78e-18  5.19e-01 -1.45e-17 -6.06e-17 -1.20e+00
41   1.93e-16  3.64e-17 -1.17e-17 -5.89e-01  3.49e-17  8.13e-17  1.36e+00
42   8.07e-18  6.38e-17 -1.20e-17 -5.04e-01  1.96e-17  3.96e-17  1.16e+00
43   1.51e-16  4.96e-17 -1.81e-17 -1.83e-16 -6.42e-17  8.37e-17 -1.21e+00
44  -9.66e-17 -1.08e-16 -8.76e-18 -2.58e-16 -4.32e-18  3.21e-17 -1.03e+00
45  -1.78e-16 -7.22e-18 -3.84e-17  3.24e-16  1.64e-17  1.19e-16  1.32e+00
46  -1.72e-16 -2.81e-17  4.60e-17  3.79e-16  1.01e-16 -1.85e-15  4.12e+00
47   1.57e-16  1.01e-17 -2.04e-17 -2.57e-16  9.44e-17 -8.19e-17 -1.37e+00
48   1.08e-16  2.73e-17 -8.49e-18 -2.38e-16 -2.86e-17 -4.42e-17 -1.30e+00
49  -7.67e-19 -2.09e-18  2.46e-18  4.78e-02 -1.60e-18 -1.23e-17  1.10e-01
50  -2.21e-18 -1.08e-18 -6.80e-19 -1.10e-02  3.02e-19 -3.45e-18 -2.55e-02
51  -3.66e-16 -2.92e-17 -5.17e-17  9.72e-01 -8.04e-18  3.90e-16  2.24e+00
52   2.26e-16  3.59e-17 -7.35e-17 -1.08e+00  2.20e-17  6.03e-16 -2.51e+00
53  -1.03e-18 -1.26e-19  2.81e-19  3.68e-03 -2.65e-20  5.08e-19  8.50e-03
54  -1.15e-17 -3.65e-18  3.15e-18  5.52e-02  7.62e-19  2.56e-17  1.27e-01
55  -7.90e-16 -1.14e-01 -4.37e-19  1.53e-17 -9.58e-19  3.28e-17  2.64e-01
56  -4.66e-16 -2.47e-01 -2.54e-18  3.77e-17 -1.23e-18 -3.35e-18  5.71e-01
57  -7.35e-17 -4.78e-02 -9.26e-19  3.95e-18  9.30e-19  2.30e-18  1.10e-01
58   9.46e-16  6.36e-01  6.98e-18 -5.75e-17  8.04e-18  2.56e-16 -1.47e+00
59  -1.55e-16 -9.20e-02 -3.66e-19  7.00e-18 -2.53e-18 -1.04e-18  2.13e-01
60  -1.98e-16 -1.22e-01 -2.45e-18  6.00e-18  2.53e-18 -1.45e-17  2.81e-01
61  -2.75e-16 -4.73e-18 -2.68e-19 -6.98e-19 -5.87e-19  3.35e-17  1.62e-01
62  -5.06e-17 -3.94e-18  4.15e-19  4.54e-18  2.01e-19 -3.34e-18 -9.35e-02
63   1.12e-16  8.74e-18 -1.35e-18 -9.54e-19  1.36e-18 -3.36e-18  1.62e-01
64  -2.80e-16 -1.68e-17  1.98e-18  9.71e-18  2.29e-18  7.27e-17 -4.17e-01
65   3.50e-17  2.43e-18 -1.02e-19 -2.08e-19 -7.09e-19  2.18e-18  5.95e-02
66   7.76e-17  2.12e-18 -1.11e-18 -1.26e-18  1.15e-18  2.53e-17  1.27e-01
67   6.87e-16 -1.84e-01  7.06e-19  1.84e-18  1.55e-18 -5.29e-17 -4.26e-01
68  -2.70e-16 -2.07e-01  2.12e-18 -1.66e-18  1.02e-18  1.27e-17 -4.77e-01
69  -1.95e-16 -1.18e-01  2.28e-18  1.61e-18 -2.29e-18  5.66e-18 -2.72e-01
70   1.42e-15  8.33e-01 -9.15e-18 -4.75e-18 -1.05e-17 -4.95e-16  1.92e+00
71  -1.78e-16 -1.18e-01  4.68e-19  8.03e-18  3.24e-18  4.17e-18 -2.72e-01
72  -2.76e-16 -1.77e-01  3.57e-18  1.68e-17 -3.68e-18 -1.30e-17 -4.09e-01
73  -8.01e-17  1.05e-18 -1.85e-19  5.55e-18 -4.17e-02 -5.96e-18  9.63e-02
74  -3.24e-17 -5.79e-19  3.85e-19  1.89e-18 -2.70e-02  4.64e-18  6.23e-02
75   1.31e-17 -3.35e-20 -5.94e-19 -2.75e-18  3.93e-02 -1.34e-17 -9.07e-02
76   6.05e-17  1.17e-19 -2.17e-18 -7.99e-18  1.20e-01 -1.83e-17 -2.78e-01
77  -4.33e-17  1.37e-19  1.48e-18  2.70e-18 -5.64e-02  1.42e-17  1.30e-01
78  -1.81e-17 -2.21e-19  5.35e-19 -9.61e-20 -3.43e-02 -3.32e-18  7.93e-02
79  -1.84e-17  4.03e-19 -7.06e-20 -4.73e-19 -2.06e-18 -5.35e-18  3.68e-02
80  -1.96e-17 -9.74e-19  6.47e-19  1.58e-19  4.54e-19 -5.28e-18  1.05e-01
81  -1.86e-17 -3.66e-20 -6.50e-19 -3.24e-18  4.48e-18 -1.05e-17 -9.92e-02
82   2.27e-18 -8.36e-21  1.55e-19 -4.16e-19  3.77e-19 -3.47e-19  1.98e-02
83   1.30e-18 -3.28e-20 -3.53e-19  5.80e-19  1.55e-18 -2.42e-18 -3.12e-02
84  -1.95e-18  8.69e-20 -2.10e-19 -3.52e-20  1.26e-18  3.90e-18 -3.12e-02
85   6.66e-17 -1.46e-18  2.55e-19 -5.53e-18 -5.77e-02  1.38e-17 -1.33e-01
86   3.14e-17  1.55e-18 -1.03e-18 -2.38e-18 -7.24e-02  1.46e-18 -1.67e-01
87   3.54e-17  7.01e-20  1.24e-18  2.69e-18  8.22e-02  2.01e-17  1.90e-01
88   2.94e-17 -1.09e-19  2.02e-18  3.25e-18  1.12e-01 -4.52e-18  2.58e-01
89   6.70e-20 -1.04e-19 -1.12e-18 -4.52e-19 -4.29e-02 -4.60e-18 -9.92e-02
90  -4.98e-18  1.34e-19 -3.25e-19  8.35e-19 -2.09e-02  6.03e-18 -4.82e-02
91   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00 -1.36e-16
92  -2.06e-17  3.30e-19 -7.36e-02 -3.21e-18 -5.83e-19  4.36e-18  1.70e-01
93  -3.37e-18 -3.91e-19  5.89e-02  1.90e-18 -2.41e-19 -7.08e-19 -1.36e-01
94   1.31e-17 -7.80e-19  1.18e-01  1.53e-18 -1.01e-19 -2.24e-17 -2.72e-01
95  -1.89e-17  1.31e-19 -1.03e-01 -6.51e-18  1.48e-18 -8.70e-18  2.38e-01
96   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00 -1.36e-16
97   4.95e-18 -2.41e-19  1.80e-18 -4.43e-18 -5.14e-19 -4.84e-18 -6.80e-02
98   1.59e-17 -1.98e-19  2.13e-18 -2.32e-18  3.50e-19  1.63e-18 -1.02e-01
99   1.59e-18  1.47e-19 -3.89e-19  8.79e-19  9.05e-20 -1.86e-18  5.10e-02
100 -1.56e-17  1.07e-18  1.29e-17 -9.89e-18  1.38e-19  4.64e-17  3.74e-01
101  2.14e-17 -1.03e-19  3.40e-18 -7.24e-19 -1.16e-18  1.46e-17 -1.87e-01
102  2.83e-18 -8.44e-20 -2.85e-19  1.03e-18  2.24e-19  1.11e-17 -6.80e-02
103 -1.68e-18  2.41e-19  2.94e-02  1.60e-18  5.14e-19  4.84e-18  6.80e-02
104  7.34e-18 -1.32e-19 -2.94e-02 -1.55e-18  2.33e-19  1.09e-18 -6.80e-02
105  3.20e-18  2.44e-19  3.68e-02  2.35e-18  1.51e-19  4.42e-19  8.50e-02
106  3.59e-18 -2.92e-19 -4.42e-02 -3.67e-18 -3.77e-20 -8.40e-18 -1.02e-01
107  3.39e-18 -2.81e-20 -2.21e-02 -7.28e-19 -3.17e-19  3.99e-18 -5.10e-02
108  4.39e-19  8.44e-20  2.94e-02  1.80e-18 -2.24e-19 -8.30e-18  6.80e-02
       cov.r   cook.d   hat inf
1   1.74e+00 1.74e-02 0.444    
2   1.04e+00 2.77e-02 0.444    
3   1.19e-02 1.14e-01 0.444   *
4   6.32e-01 3.79e-02 0.444    
5   2.32e+00 1.15e-02 0.444    
6   1.85e+00 1.61e-02 0.444    
7   3.98e+00 2.86e-04 0.444   *
8   3.94e+00 4.78e-04 0.444   *
9   2.74e+00 8.00e-03 0.444    
10  4.00e+00 1.63e-04 0.444   *
11  3.94e+00 4.78e-04 0.444   *
12  3.71e+00 1.73e-03 0.444   *
13  1.38e+00 2.22e-02 0.444    
14  7.11e-01 3.55e-02 0.444    
15  2.50e-04 1.83e-01 0.444   *
16  4.89e-01 4.30e-02 0.444    
17  1.80e+00 1.67e-02 0.444    
18  1.01e+00 2.84e-02 0.444    
19  3.74e+00 1.57e-03 0.444   *
20  3.89e+00 7.40e-04 0.444   *
21  4.03e+00 6.12e-06 0.444   *
22  2.28e+00 1.18e-02 0.444    
23  3.94e+00 4.96e-04 0.444   *
24  3.94e+00 4.96e-04 0.444   *
25  4.00e+00 1.85e-04 0.444   *
26  4.03e+00 1.38e-05 0.444   *
27  4.03e+00 1.38e-05 0.444   *
28  3.88e+00 8.09e-04 0.444   *
29  3.95e+00 4.42e-04 0.444   *
30  3.95e+00 4.42e-04 0.444   *
31  3.90e+00 6.75e-04 0.444   *
32  3.85e+00 9.56e-04 0.444   *
33  4.03e+00 3.82e-05 0.444   *
34  1.62e+00 1.89e-02 0.444    
35  3.69e+00 1.87e-03 0.444   *
36  3.69e+00 1.87e-03 0.444   *
37  1.22e+00 2.47e-02 0.444    
38  1.31e+00 2.31e-02 0.444    
39  4.48e-06 2.48e-01 0.444   *
40  9.55e-01 2.96e-02 0.444    
41  6.37e-01 3.77e-02 0.444    
42  1.04e+00 2.79e-02 0.444    
43  9.35e-01 3.00e-02 0.444    
44  1.38e+00 2.20e-02 0.444    
45  7.17e-01 3.53e-02 0.444    
46  1.56e-06 2.65e-01 0.444   *
47  6.22e-01 3.82e-02 0.444    
48  7.51e-01 3.44e-02 0.444    
49  3.98e+00 2.59e-04 0.444   *
50  4.03e+00 1.38e-05 0.444   *
51  3.11e-02 9.64e-02 0.444    
52  1.01e-02 1.17e-01 0.444   *
53  4.03e+00 1.53e-06 0.444   *
54  3.97e+00 3.44e-04 0.444   *
55  3.76e+00 1.47e-03 0.444   *
56  2.90e+00 6.87e-03 0.444    
57  3.98e+00 2.59e-04 0.444   *
58  4.72e-01 4.37e-02 0.444    
59  3.85e+00 9.56e-04 0.444   *
60  3.72e+00 1.67e-03 0.444   *
61  3.93e+00 5.52e-04 0.444   *
62  4.00e+00 1.85e-04 0.444   *
63  3.93e+00 5.52e-04 0.444   *
64  3.38e+00 3.67e-03 0.444    
65  4.02e+00 7.50e-05 0.444   *
66  3.97e+00 3.44e-04 0.444   *
67  3.36e+00 3.82e-03 0.444    
68  3.20e+00 4.80e-03 0.444    
69  3.74e+00 1.57e-03 0.444   *
70  1.08e-01 7.27e-02 0.444    
71  3.74e+00 1.57e-03 0.444   *
72  3.40e+00 3.52e-03 0.444   *
73  4.00e+00 1.97e-04 0.444   *
74  4.02e+00 8.23e-05 0.444   *
75  4.00e+00 1.74e-04 0.444   *
76  3.73e+00 1.63e-03 0.444   *
77  3.96e+00 3.60e-04 0.444   *
78  4.01e+00 1.33e-04 0.444   *
79  4.03e+00 2.87e-05 0.444   *
80  3.99e+00 2.33e-04 0.444   *
81  3.99e+00 2.08e-04 0.444   *
82  4.03e+00 8.33e-06 0.444   *
83  4.03e+00 2.06e-05 0.444   *
84  4.03e+00 2.06e-05 0.444   *
85  3.96e+00 3.76e-04 0.444   *
86  3.92e+00 5.92e-04 0.444   *
87  3.89e+00 7.63e-04 0.444   *
88  3.77e+00 1.41e-03 0.444   *
89  3.99e+00 2.08e-04 0.444   *
90  4.02e+00 4.91e-05 0.444   *
91  4.03e+00 3.91e-34 0.444   *
92  3.92e+00 6.12e-04 0.444   *
93  3.96e+00 3.92e-04 0.444   *
94  3.74e+00 1.57e-03 0.444   *
95  3.81e+00 1.20e-03 0.444   *
96  4.03e+00 3.91e-34 0.444   *
97  4.01e+00 9.79e-05 0.444   *
98  3.99e+00 2.20e-04 0.444   *
99  4.02e+00 5.51e-05 0.444   *
100 3.50e+00 2.96e-03 0.444   *
101 3.89e+00 7.40e-04 0.444   *
102 4.01e+00 9.79e-05 0.444   *
103 4.01e+00 9.79e-05 0.444   *
104 4.01e+00 9.79e-05 0.444   *
105 4.00e+00 1.53e-04 0.444   *
106 3.99e+00 2.20e-04 0.444   *
107 4.02e+00 5.51e-05 0.444   *
108 4.01e+00 9.79e-05 0.444   *
influenceIndexPlot(modelo.dca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos de la infestación de la enfermedad son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos de la infestación de la enfermedad no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1     -0.03541614      2.061107  0.2960
   2     -0.54313336      3.061097  0.0000
   3     -0.17331899      2.257845  0.3004
   4      0.31145869      1.267165  0.0020
   5      0.22040162      1.442840  0.0656
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dca
DW = 2.0611, p-value = 0.2925
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos de la infestación de la enfermedad son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos de la infestación de la enfermedad es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos de la infestación de la enfermedad es similar a la función normal}\)

shapiro.test(rstudent(modelo.dca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dca)
W = 0.83592, p-value = 1.346e-09
ad.test(rstudent(modelo.dca))

    Anderson-Darling normality test

data:  rstudent(modelo.dca)
A = 6.6044, p-value = 2.676e-16
lillie.test(rstudent(modelo.dca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dca)
D = 0.22598, p-value = 7.152e-15
ks.test(rstudent(modelo.dca), "pnorm",
        alternative = "two.sided")

    Asymptotic one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dca)
D = 0.21702, p-value = 7.634e-05
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dca)
W = 1.3725, p-value = 7.37e-10
pearson.test(rstudent(modelo.dca))

    Pearson chi-square normality test

data:  rstudent(modelo.dca)
P = 118.07, p-value < 2.2e-16
sf.test(rstudent(modelo.dca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dca)
W = 0.82123, p-value = 7.281e-09

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos de la infestación de la enfermedad es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza de la infestación de la enfermedad es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza de la infestación de la enfermedad no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 130.6704, Df = 1, p = < 2.22e-16
bptest(modelo.dca)

    studentized Breusch-Pagan test

data:  modelo.dca
BP = 73.988, df = 47, p-value = 0.007234
bptest(modelo.dca, studentize = F)

    Breusch-Pagan test

data:  modelo.dca
BP = 242.17, df = 47, p-value < 2.2e-16
olsrr::ols_test_breusch_pagan(modelo.dca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

            Data              
 -----------------------------
 Response : y 
 Variables: fitted values of y 

         Test Summary           
 -------------------------------
 DF            =    1 
 Chi2          =    130.6704 
 Prob > Chi2   =    2.923296e-30 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza de la infestación de la enfermedad es constante con respecto a los valores ajustados de la infestación de la enfermedad.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto a la infestación de la enfermedad, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dca %>% gvlma()

Call:
lm(formula = y ~ variedad * tiempo + rep:variedad, data = data)

Coefficients:
                 (Intercept)            variedadDuraznillo  
                     -1.7778                       15.6111  
               variedadNegra              variedadPukaÑawi  
                     21.7778                       -2.3889  
              variedadTumbay            variedadYanaPepino  
                     18.8889                       13.4444  
                    tiempos4                     tiempos10  
                     -9.6667                       81.3333  
                   tiempos12                     tiempos15  
                     81.0000                      -12.6667  
                   tiempos16   variedadDuraznillo:tiempos4  
                    -15.3333                        1.6667  
      variedadNegra:tiempos4     variedadPukaÑawi:tiempos4  
                      2.3333                        1.3333  
     variedadTumbay:tiempos4   variedadYanaPepino:tiempos4  
                      6.3333                        4.3333  
variedadDuraznillo:tiempos10       variedadNegra:tiempos10  
                    -96.3333                      -93.6667  
  variedadPukaÑawi:tiempos10      variedadTumbay:tiempos10  
                     -5.0000                      -87.6667  
variedadYanaPepino:tiempos10  variedadDuraznillo:tiempos12  
                    -92.6667                      -63.6667  
     variedadNegra:tiempos12    variedadPukaÑawi:tiempos12  
                    -79.6667                      -36.6667  
    variedadTumbay:tiempos12  variedadYanaPepino:tiempos12  
                    -85.6667                      -77.0000  
variedadDuraznillo:tiempos15       variedadNegra:tiempos15  
                     -5.3333                       -5.0000  
  variedadPukaÑawi:tiempos15      variedadTumbay:tiempos15  
                     -4.3333                       -5.0000  
variedadYanaPepino:tiempos15  variedadDuraznillo:tiempos16  
                     -2.0000                       -4.0000  
     variedadNegra:tiempos16    variedadPukaÑawi:tiempos16  
                     -4.6667                       -3.0000  
    variedadTumbay:tiempos16  variedadYanaPepino:tiempos16  
                     -3.3333                        0.6667  
        variedadCanchan:rep2       variedadDuraznillo:rep2  
                     11.5000                        3.0000  
          variedadNegra:rep2         variedadPukaÑawi:rep2  
                      1.3333                       47.5000  
         variedadTumbay:rep2       variedadYanaPepino:rep2  
                      2.1667                        0.1667  
        variedadCanchan:rep3       variedadDuraznillo:rep3  
                     40.8333                       13.5000  
          variedadNegra:rep3         variedadPukaÑawi:rep3  
                     -1.3333                       21.0000  
         variedadTumbay:rep3       variedadYanaPepino:rep3  
                      5.5000                        8.8333  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                      Value   p-value                   Decision
Global Stat        184.8215 0.000e+00 Assumptions NOT satisfied!
Skewness             0.7003 4.027e-01    Assumptions acceptable.
Kurtosis            93.0064 0.000e+00 Assumptions NOT satisfied!
Link Function       71.1713 0.000e+00 Assumptions NOT satisfied!
Heteroscedasticity  19.9435 7.976e-06 Assumptions NOT satisfied!

Análisis de varianza

\[Y_{ijk} = \mu + \tau_{i} + \beta_{j} + (\tau\beta)_{ij} + \text{Error}(\tau\text{rep})_{i(k)} + \epsilon_{ijk}\]

\[\hat{Y}_{ijk} = \mu + \tau_{i} + \beta_{j} + (\tau\beta)_{ij} + \text{Error}(\tau\text{rep})_{i(k)}\]

Dónde:

\(Y_{ijk}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijk}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor variedad.

\(\text{Error}(\tau\text{rep})_{i(k)}\) = Efecto del i-ésimo nivel de variedad en el k-ésimo nivel de repetición.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor tiempo.

\((\tau\beta)_{ij}\) = Efecto de la interacción entre el i-ésimo nivel del factor variedad y el j-ésimo nivel del factor tiempo.

\(\epsilon_{ijk}\) = Residuo observado del modelo.

Pruebas de hipótesis

Para el factor A (variedad):

\(H_0: \tau_{A1} = \tau_{A2} = ... = \tau_{A6} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (tiempo):

\(H_0: \beta_{B1} = \beta_{B2} = ... = \tau_{B6} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dca, test = "F")
Analysis of Variance Table

Response: y
                Df Sum Sq Mean Sq F value    Pr(>F)    
variedad         5  13725  2745.0  5.0396 0.0006392 ***
tiempo           5  27916  5583.1 10.2501 3.922e-07 ***
variedad:tiempo 25  33778  1351.1  2.4805 0.0021249 ** 
variedad:rep    12  13142  1095.2  2.0106 0.0387578 *  
Residuals       60  32681   544.7                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(Zona/rep)” en el caso de efectos aleatorios o “Error(Zona:rep)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos.

aov(y ~ variedad*tiempo + Error(variedad:rep), data = data) -> aov.dca
summary(aov.dca)

Error: variedad:rep
          Df Sum Sq Mean Sq F value Pr(>F)  
variedad   5  13725    2745   2.507 0.0892 .
Residuals 12  13142    1095                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Error: Within
                Df Sum Sq Mean Sq F value   Pr(>F)    
tiempo           5  27916    5583  10.250 3.92e-07 ***
variedad:tiempo 25  33778    1351   2.481  0.00212 ** 
Residuals       60  32681     545                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
broom::tidy(aov.dca)
# A tibble: 5 × 7
  stratum      term               df  sumsq meansq statistic      p.value
  <chr>        <chr>           <dbl>  <dbl>  <dbl>     <dbl>        <dbl>
1 variedad:rep variedad            5 13725.  2745.      2.51  0.0892     
2 variedad:rep Residuals          12 13142.  1095.     NA    NA          
3 Within       tiempo              5 27916.  5583.     10.3   0.000000392
4 Within       variedad:tiempo    25 33778.  1351.      2.48  0.00212    
5 Within       Residuals          60 32681.   545.     NA    NA          

Valor de la tabla de F para el factor variedad con una significancia de 0.05.

qf(0.95, 5, 12)
[1] 3.105875

Valor de la tabla de F para el factor tiempo con una significancia de 0.05.

qf(0.95, 5, 60)
[1] 2.36827

Conclusión.

Con respecto al Factor variedad: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor Zona tienen un efecto sobre la infestación de la enfermedad estadísticamente similar a 0.

Con respecto al Factor tiempo: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor tiempo posee un efecto sobre la infestación de la enfermedad estadísticamente diferente a 0.

Con respecto a la interacción variedad*tiempo: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos una interacción entre variedad y tiempo tuvo un efecto de antagonismo o sinergismo en infestación de la enfermedad.

agricolae::cv.model(modelo.dca)
[1] 127.6884

Comparaciones de medias para los efectos principales del Factor variedad

get_df_ea <- function(object) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  df_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(":", stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(df)
  return(df_rep_A_residuals)
}
get_df_ea(aov.dca)
[1] 12
get_mse_ea <- function(object) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  meansq_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(":", stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(meansq)
  return(meansq_rep_A_residuals)
}
get_mse_ea(aov.dca)
[1] 1095.157
data %>% with(LSD.test(
  y, # Cambiar según nombre de variable respuesta
  variedad, # Cambiar según nombre de variable independiente
  DFerror = get_df_ea(aov.dca), 
  MSerror = get_mse_ea(aov.dca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: y ~ variedad

LSD t Test for y 

Mean Square Error:  1095.157 

variedad,  means and individual ( 95 %) CI

                   y       std  r       LCL      UCL Min Max
Canchan    36.444444 53.575919 18 19.449414 53.43947   0 178
Duraznillo 12.166667 19.147262 18 -4.828364 29.16170   0  81
Negra      10.666667  8.977095 18 -6.328364 27.66170   0  30
PukaÑawi   31.500000 53.140491 18 14.504970 48.49503   0 157
Tumbay     11.222222  8.142521 18 -5.772808 28.21725   0  23
YanaPepino  7.666667 10.803050 18 -9.328364 24.66170   0  43

Alpha: 0.05 ; DF Error: 12
Critical Value of t: 2.178813 

least Significant Difference: 24.0346 

Treatments with the same letter are not significantly different.

                   y groups
Canchan    36.444444      a
PukaÑawi   31.500000     ab
Duraznillo 12.166667      b
Tumbay     11.222222      b
Negra      10.666667      b
YanaPepino  7.666667      b

Comparaciones de medias para los efectos principales del Factor tiempo

data %>% with(LSD.test(
  y, # Cambiar según nombre de variable respuesta
  tiempo, # Cambiar según nombre de variable independiente
  DFerror = df.residual(modelo.dca), 
  MSerror = dvmisc::get_mse(modelo.dca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: y ~ tiempo

LSD t Test for y 

Mean Square Error:  544.6907 

tiempo,  means and individual ( 95 %) CI

             y        std  r           LCL      UCL Min Max
s10 36.7777778 56.8667747 18  25.774212964 47.78134   0 178
s12 41.8888889 47.1142402 18  30.885324075 52.89245   1 157
s15  1.7222222  2.7824144 18  -9.281342591 12.72579   0   9
s16  0.2777778  0.7519039 18 -10.725787036 11.28134   0   3
s3  18.0000000  2.8697202 18   6.996435187 29.00356  10  20
s4  11.0000000  4.4325003 18  -0.003564813 22.00356   3  18

Alpha: 0.05 ; DF Error: 60
Critical Value of t: 2.000298 

least Significant Difference: 15.56139 

Treatments with the same letter are not significantly different.

             y groups
s12 41.8888889      a
s10 36.7777778      a
s3  18.0000000      b
s4  11.0000000     bc
s15  1.7222222      c
s16  0.2777778      c

Comparaciones de medias para las interacciones

Para los niveles del factor A dentro del nivel B1:

  • A1 vs A2:

\(H_0: \mu_{A1} - \mu_{A2} = 0\)

\(H_1: \mu_{A1} - \mu_{A2} \neq 0\)

  • A5 vs A6:

\(H_0: \mu_{A5} - \mu_{A6} = 0\)

\(H_1: \mu_{A5} - \mu_{A6} \neq 0\)

Para los niveles del factor B dentro del nivel A1:

  • B1 vs B2:

\(H_0: \mu_{B1} - \mu_{B2} = 0\)

\(H_1: \mu_{B1} - \mu_{B2} \neq 0\)

  • B5 vs B6:

\(H_0: \mu_{B5} - \mu_{B6} = 0\)

\(H_1: \mu_{B5} - \mu_{B6} \neq 0\)

NOTA: Repetir este proceso para cada nivel de A y cada nivel de B.

Análisis de varianza para interacción de dos factores con el paquete phia

Comparación de los niveles de B dentro de cada nivel de A

phia::testInteractions(modelo.dca,
                       fixed = "variedad",
                       across = "tiempo",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
           tiempo1 tiempo2 tiempo3 tiempo4 tiempo5 Df Sum of Sq       F
   Canchan  15.333  5.6667  96.667  96.333  2.6667  5     33224 12.1994
Duraznillo  19.333 11.3333   4.333  36.667  1.3333  5      2937  1.0785
     Negra  20.000 12.6667   7.667  21.333  2.3333  5      1191  0.4374
  PukaÑawi  18.333 10.0000  94.667  62.667  1.3333  5     22496  8.2600
    Tumbay  18.667 15.3333  12.333  14.000  1.0000  5       917  0.3367
YanaPepino  14.667  9.3333   3.333  18.667  0.0000  5       927  0.3405
Residuals                                          60     32681        
              Pr(>F)    
   Canchan 3.583e-08 ***
Duraznillo    0.3815    
     Negra    0.8206    
  PukaÑawi 5.502e-06 ***
    Tumbay    0.8887    
YanaPepino    0.8863    
Residuals               
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Comparación de los niveles de A dentro de cada nivel de B

phia::testInteractions(modelo.dca,
                       fixed = "tiempo",
                       across = "variedad",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
          variedad1 variedad2 variedad3 variedad4 variedad5 Df Sum of Sq
 s3           1.000    4.6667    5.3333     4.000    5.0000  5        77
 s4          -3.333    2.0000    3.3333     1.000    7.0000  5       179
s10          93.667    1.0000    4.3333    91.667   10.0000  5     31754
s12          78.000   18.0000    2.6667    44.333   -3.6667  5     15475
s15           3.000    1.3333    2.3333     1.667    2.0000  5        16
s16           0.333    0.0000    0.0000     0.333    1.0000  5         2
Residuals                                                   60     32681
                F    Pr(>F)    
 s3        0.0282 0.9996019    
 s4        0.0656 0.9969278    
s10       11.6596 6.827e-08 ***
s12        5.6822 0.0002355 ***
s15        0.0057 0.9999922    
s16        0.0008 0.9999999    
Residuals                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Plot de interacciones

phia::interactionMeans(model = modelo.dca,
                       factors = c("variedad","tiempo")) %>%
  plot()

Comparaciones de medias de los niveles de B dentro de cada nivel de A

datos_filtrados <- filter_by_2factor_level(data = data,
                       factor_name1 = variedad,
                       factor_name2 = tiempo)
multcomp.test_2factors <- function(object, respuesta, factor_name1, factor_name2, test, aov, reverse){
  
  # Función auxiliar para aplicar la prueba de comparaciones múltiples a un data frame
  multcomp_df <- function(df, respuesta, factor_name, test, aov){
    if (test == "LSD") {
      comp <- LSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "HSD") {
      comp <- HSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "duncan") {
      comp <- duncan.test(df[[respuesta]],
                          df[[factor_name]],
                          DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                          group=TRUE,
                          main = NULL,
                          console=FALSE)[[6]]
    } else if (test == "SNK") {
      comp <- SNK.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[6]]
    } else {
      stop("Test no válido. Los tests disponibles son LSD, HSD, duncan, y SNK.")
    }
    if (reverse == TRUE) {
      comp <- comp %>%
        dplyr::mutate(groups = rev(groups))
    } else if (reverse == FALSE) {
      comp <- comp
    } else {
      stop("Test no válido. Los tests disponibles son LSD, HSD, duncan, y SNK.")
    }
    return(comp %>%
             rename("y" = "df[[respuesta]]")
           )
  }
  
  # Aplicar la prueba de comparaciones múltiples a todos los data frames dentro de filters1
  comp_filters1 <- lapply(object[[1]], function(df){
    multcomp_df(df, respuesta, factor_name2, test, aov) %>%
      arrange(row.names(.)) %>%
      rownames_to_column(var = "x") %>%
      relocate(x)
  })
  
  # Aplicar la prueba de comparaciones múltiples a todos los data frames dentro de filters2
  comp_filters2 <- lapply(object[[2]], function(df){
    multcomp_df(df, respuesta, factor_name1, test, aov) %>%
      dplyr::arrange(row.names(.)) %>%
      rownames_to_column(var = "x") %>%
      relocate(x) %>%
      dplyr::mutate(groups = toupper(groups))
  })
  
  row.names(comp_filters1) <- NULL
  row.names(comp_filters2) <- NULL
  # Retornar una lista con las comparaciones múltiples para cada data frame
  result <- list()
  result[[as.name(substitute(factor_name1))]] <- comp_filters1
  result[[as.name(substitute(factor_name2))]] <- comp_filters2
  return(#list(#"Comparación de los niveles del factor B dentro de cada nivel del factor A",
         result#[[1]],
         # "Comparación de los niveles del factor A dentro de cada nivel del factor B",
         # result[[2]]
         # )
  )
}
multcomp.test_2factors(
  object = datos_filtrados,
  respuesta = "y",
  factor_name1 = "variedad",
  factor_name2 = "tiempo",
  test = "LSD",
  aov = modelo.dca,
  reverse = TRUE) -> result.comp
result.comp
$variedad
$variedad$Canchan
    x          y groups
1 s10 97.0000000      b
2 s12 96.6666667      b
3 s15  3.0000000      a
4 s16  0.3333333      a
5  s3 15.6666667      b
6  s4  6.0000000      b

$variedad$Duraznillo
    x         y groups
1 s10  4.333333      a
2 s12 36.666667      a
3 s15  1.333333      a
4 s16  0.000000      a
5  s3 19.333333      a
6  s4 11.333333      a

$variedad$Negra
    x         y groups
1 s10  7.666667      a
2 s12 21.333333      a
3 s15  2.333333      a
4 s16  0.000000      a
5  s3 20.000000      a
6  s4 12.666667      a

$variedad$PukaÑawi
    x          y groups
1 s10 95.0000000      b
2 s12 63.0000000      b
3 s15  1.6666667      a
4 s16  0.3333333      a
5  s3 18.6666667      b
6  s4 10.3333333      b

$variedad$Tumbay
    x        y groups
1 s10 13.33333      a
2 s12 15.00000      a
3 s15  2.00000      a
4 s16  1.00000      a
5  s3 19.66667      a
6  s4 16.33333      a

$variedad$YanaPepino
    x         y groups
1 s10  3.333333      a
2 s12 18.666667      a
3 s15  0.000000      a
4 s16  0.000000      a
5  s3 14.666667      a
6  s4  9.333333      a


$tiempo
$tiempo$s3
           x        y groups
1    Canchan 15.66667      A
2 Duraznillo 19.33333      A
3      Negra 20.00000      A
4   PukaÑawi 18.66667      A
5     Tumbay 19.66667      A
6 YanaPepino 14.66667      A

$tiempo$s4
           x         y groups
1    Canchan  6.000000      A
2 Duraznillo 11.333333      A
3      Negra 12.666667      A
4   PukaÑawi 10.333333      A
5     Tumbay 16.333333      A
6 YanaPepino  9.333333      A

$tiempo$s10
           x         y groups
1    Canchan 97.000000      B
2 Duraznillo  4.333333      A
3      Negra  7.666667      B
4   PukaÑawi 95.000000      B
5     Tumbay 13.333333      B
6 YanaPepino  3.333333      A

$tiempo$s12
           x        y groups
1    Canchan 96.66667      C
2 Duraznillo 36.66667      C
3      Negra 21.33333     BC
4   PukaÑawi 63.00000      C
5     Tumbay 15.00000      A
6 YanaPepino 18.66667     AB

$tiempo$s15
           x        y groups
1    Canchan 3.000000      A
2 Duraznillo 1.333333      A
3      Negra 2.333333      A
4   PukaÑawi 1.666667      A
5     Tumbay 2.000000      A
6 YanaPepino 0.000000      A

$tiempo$s16
           x         y groups
1    Canchan 0.3333333      A
2 Duraznillo 0.0000000      A
3      Negra 0.0000000      A
4   PukaÑawi 0.3333333      A
5     Tumbay 1.0000000      A
6 YanaPepino 0.0000000      A
# Convertir la lista a un data frame
df <- result.comp %>%
  reshape2::melt() %>% 
  ungroup() %>%
  dplyr::select(-variable) %>%
  relocate("Factor" = "L1",
           "Nivel" = "L2",
           x,
           "y" = "value",
           groups) #%>%
  # group_by(Factor, Nivel) %>%
  # dplyr::mutate(groups = rev(groups)) %>%
  # dplyr::ungroup()
df
     Factor      Nivel          x          y groups
1  variedad    Canchan        s10 97.0000000      b
2  variedad    Canchan        s12 96.6666667      b
3  variedad    Canchan        s15  3.0000000      a
4  variedad    Canchan        s16  0.3333333      a
5  variedad    Canchan         s3 15.6666667      b
6  variedad    Canchan         s4  6.0000000      b
7  variedad Duraznillo        s10  4.3333333      a
8  variedad Duraznillo        s12 36.6666667      a
9  variedad Duraznillo        s15  1.3333333      a
10 variedad Duraznillo        s16  0.0000000      a
11 variedad Duraznillo         s3 19.3333333      a
12 variedad Duraznillo         s4 11.3333333      a
13 variedad      Negra        s10  7.6666667      a
14 variedad      Negra        s12 21.3333333      a
15 variedad      Negra        s15  2.3333333      a
16 variedad      Negra        s16  0.0000000      a
17 variedad      Negra         s3 20.0000000      a
18 variedad      Negra         s4 12.6666667      a
19 variedad   PukaÑawi        s10 95.0000000      b
20 variedad   PukaÑawi        s12 63.0000000      b
21 variedad   PukaÑawi        s15  1.6666667      a
22 variedad   PukaÑawi        s16  0.3333333      a
23 variedad   PukaÑawi         s3 18.6666667      b
24 variedad   PukaÑawi         s4 10.3333333      b
25 variedad     Tumbay        s10 13.3333333      a
26 variedad     Tumbay        s12 15.0000000      a
27 variedad     Tumbay        s15  2.0000000      a
28 variedad     Tumbay        s16  1.0000000      a
29 variedad     Tumbay         s3 19.6666667      a
30 variedad     Tumbay         s4 16.3333333      a
31 variedad YanaPepino        s10  3.3333333      a
32 variedad YanaPepino        s12 18.6666667      a
33 variedad YanaPepino        s15  0.0000000      a
34 variedad YanaPepino        s16  0.0000000      a
35 variedad YanaPepino         s3 14.6666667      a
36 variedad YanaPepino         s4  9.3333333      a
37   tiempo         s3    Canchan 15.6666667      A
38   tiempo         s3 Duraznillo 19.3333333      A
39   tiempo         s3      Negra 20.0000000      A
40   tiempo         s3   PukaÑawi 18.6666667      A
41   tiempo         s3     Tumbay 19.6666667      A
42   tiempo         s3 YanaPepino 14.6666667      A
43   tiempo         s4    Canchan  6.0000000      A
44   tiempo         s4 Duraznillo 11.3333333      A
45   tiempo         s4      Negra 12.6666667      A
46   tiempo         s4   PukaÑawi 10.3333333      A
47   tiempo         s4     Tumbay 16.3333333      A
48   tiempo         s4 YanaPepino  9.3333333      A
49   tiempo        s10    Canchan 97.0000000      B
50   tiempo        s10 Duraznillo  4.3333333      A
51   tiempo        s10      Negra  7.6666667      B
52   tiempo        s10   PukaÑawi 95.0000000      B
53   tiempo        s10     Tumbay 13.3333333      B
54   tiempo        s10 YanaPepino  3.3333333      A
55   tiempo        s12    Canchan 96.6666667      C
56   tiempo        s12 Duraznillo 36.6666667      C
57   tiempo        s12      Negra 21.3333333     BC
58   tiempo        s12   PukaÑawi 63.0000000      C
59   tiempo        s12     Tumbay 15.0000000      A
60   tiempo        s12 YanaPepino 18.6666667     AB
61   tiempo        s15    Canchan  3.0000000      A
62   tiempo        s15 Duraznillo  1.3333333      A
63   tiempo        s15      Negra  2.3333333      A
64   tiempo        s15   PukaÑawi  1.6666667      A
65   tiempo        s15     Tumbay  2.0000000      A
66   tiempo        s15 YanaPepino  0.0000000      A
67   tiempo        s16    Canchan  0.3333333      A
68   tiempo        s16 Duraznillo  0.0000000      A
69   tiempo        s16      Negra  0.0000000      A
70   tiempo        s16   PukaÑawi  0.3333333      A
71   tiempo        s16     Tumbay  1.0000000      A
72   tiempo        s16 YanaPepino  0.0000000      A
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # # Convertir level1 y level2 en nombres simbólicos
  # level1 <- as.name(level1)
  # level2 <- as.name(level2)
  # 
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1, level2)) %>%
    dplyr::mutate(groups = paste0(groups.y,groups.x)) %>%
    dplyr::select(!!level1,!!level2, y, groups) #%>%
    # rename(!!level1 := x,
    #        !!level2 := Nivel)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
df2 <- create_report(df = df,
               level1 = "variedad",
               level2 = "tiempo")
df2 %>% gt()
variedad tiempo y groups
Canchan s10 97.0000000 Bb
Canchan s12 96.6666667 Cb
Canchan s15 3.0000000 Ab
Canchan s16 0.3333333 Ab
Canchan s3 15.6666667 Aa
Canchan s4 6.0000000 Aa
Duraznillo s10 4.3333333 Ba
Duraznillo s12 36.6666667 Ca
Duraznillo s15 1.3333333 Aa
Duraznillo s16 0.0000000 Aa
Duraznillo s3 19.3333333 Aa
Duraznillo s4 11.3333333 Aa
Negra s10 7.6666667 Aa
Negra s12 21.3333333 ABa
Negra s15 2.3333333 Aa
Negra s16 0.0000000 Aa
Negra s3 20.0000000 Aa
Negra s4 12.6666667 Aa
PukaÑawi s10 95.0000000 Bb
PukaÑawi s12 63.0000000 Cb
PukaÑawi s15 1.6666667 Ab
PukaÑawi s16 0.3333333 Ab
PukaÑawi s3 18.6666667 Aa
PukaÑawi s4 10.3333333 Aa
Tumbay s10 13.3333333 Ba
Tumbay s12 15.0000000 BCa
Tumbay s15 2.0000000 Aa
Tumbay s16 1.0000000 Aa
Tumbay s3 19.6666667 Aa
Tumbay s4 16.3333333 Aa
YanaPepino s10 3.3333333 Aa
YanaPepino s12 18.6666667 Aa
YanaPepino s15 0.0000000 Aa
YanaPepino s16 0.0000000 Aa
YanaPepino s3 14.6666667 Aa
YanaPepino s4 9.3333333 Aa
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1,level2)) %>%
    dplyr::mutate(y = paste0(round(y,2), " ", groups.y, groups.x)) %>%
    dplyr::select(!!level1,!!level2, y)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
df3 <- create_report(df = df,
               level1 = "variedad",
               level2 = "tiempo") 
df3 %>% gt()
variedad tiempo y
Canchan s10 97 Bb
Canchan s12 96.67 Cb
Canchan s15 3 Ab
Canchan s16 0.33 Ab
Canchan s3 15.67 Aa
Canchan s4 6 Aa
Duraznillo s10 4.33 Ba
Duraznillo s12 36.67 Ca
Duraznillo s15 1.33 Aa
Duraznillo s16 0 Aa
Duraznillo s3 19.33 Aa
Duraznillo s4 11.33 Aa
Negra s10 7.67 Aa
Negra s12 21.33 ABa
Negra s15 2.33 Aa
Negra s16 0 Aa
Negra s3 20 Aa
Negra s4 12.67 Aa
PukaÑawi s10 95 Bb
PukaÑawi s12 63 Cb
PukaÑawi s15 1.67 Ab
PukaÑawi s16 0.33 Ab
PukaÑawi s3 18.67 Aa
PukaÑawi s4 10.33 Aa
Tumbay s10 13.33 Ba
Tumbay s12 15 BCa
Tumbay s15 2 Aa
Tumbay s16 1 Aa
Tumbay s3 19.67 Aa
Tumbay s4 16.33 Aa
YanaPepino s10 3.33 Aa
YanaPepino s12 18.67 Aa
YanaPepino s15 0 Aa
YanaPepino s16 0 Aa
YanaPepino s3 14.67 Aa
YanaPepino s4 9.33 Aa
df3 %>% 
 pivot_wider(names_from = tiempo,
             values_from = c(y), 
             names_glue = "{tiempo}") %>%
  dplyr::select(variedad,s3,s4,s10,s12,s15,s16) %>%
  gt()
variedad s3 s4 s10 s12 s15 s16
Canchan 15.67 Aa 6 Aa 97 Bb 96.67 Cb 3 Ab 0.33 Ab
Duraznillo 19.33 Aa 11.33 Aa 4.33 Ba 36.67 Ca 1.33 Aa 0 Aa
Negra 20 Aa 12.67 Aa 7.67 Aa 21.33 ABa 2.33 Aa 0 Aa
PukaÑawi 18.67 Aa 10.33 Aa 95 Bb 63 Cb 1.67 Ab 0.33 Ab
Tumbay 19.67 Aa 16.33 Aa 13.33 Ba 15 BCa 2 Aa 1 Aa
YanaPepino 14.67 Aa 9.33 Aa 3.33 Aa 18.67 Aa 0 Aa 0 Aa